Calculus - Week 9
So this week in Calculus was a very stressful one for most...but I got through it rather easily. On Sunday I went to Kaitlyn's house to study with Chelsea, Mamie, and Mabile and we finished our short answer packets. Monday and Tuesday we got the answers for those and revised any questions we had etc. We were having some issues with limiting on optimization problems but it turned out okay. Wednesday was the first part of the exam which was Multiple Choice. The multiple choice wasn't that bad. We were allowed to miss 5 so what I did was go through and do all of those that I knew how to do correctly instead of worrying about one particular problem. Then I went back and focused on those I was unsure of and made educated guesses. It turned out okay because I missed 4 or 5 but that was allowed so I made a 60/60. Next day we got to take the free response part. I think it was very very easy. I felt comfortable with everything about it. I knew how to do the problems and justify myself well.
All in all, all of the preparation for the exam was much needed and helped out a lot. If people didn't make as good of grades this time, maybe next time a little more preparation will help.
As far as what else we did this week, we did implicit derivatives. The reason implicit derivatives (I think anyway) are useful are for those problems that it's hard to solve for y only in terms of x. I think this will come in handy for those.
Basically implicit derivatives are nothing new at all... the steps are pretty much just this:
1. Take the derivative of both sides (implicit derivatives usually have an equals sign)
2. When you take a derivative of a y term, state that. Do so by putting y prime or dy/dx. Like ( taking the derivative of y^2 would be 2y(dy/dx) )
3. Move all of the terms that don't have a dy/dx in them to one side. Factor out a dy/dx out of all the terms that do have it, then divide to finish solving for dy/dx.
That's basically all it is. Just make sure when you are doing these is like...say you are doing product rule with like sin's and cos's...make sure you put cos(x) where its supposed to and cos(y) where its supposed to. It would really mess up problems (like the one we were working in class) if you mix this up. So take these longer derivatives slow and just avoid making silly mistakes.
Anyway, I'm going eat Taco Bell. :-)
-John
Saturday, October 17, 2009
9th post
whew... i got through the caluclus exam without to many headaches :), but by doing all of those study guides helped me to understand some problems that i didn't understand before.. one of those is tangent line.
1. take the derivative of the function... then plug the x value they give you into the derivative and get the slope.
2. If they do not give you a y value, you have to plug the x value into the original function to get it.
3. After you have all the variables, you can set the equation up into the form y-y1=slope(x-x1).
Another thing i'm feeling better about is surprisingly optimization...
1. First things first, finding the primary and secondary functions are a must, your primary function will always be what they are asking for such as (maximize area, perimeter, etc.)
2. Once you find those, use your primary function to solve for one variable.
3. Once you find that variable, you plug it into its designated spot in the secondary function, then simplify.
4. Once that is done, take the derivative, set it equal to zero and solve for the remaining variable. One variable will be solved for.
5. Once you find the remaining variable, you plug it back into the equation where you solved for the first variable. Your other variable will be solved for.
Now lets get into the stuff we learned on Friday: implicit derivatives
Basically, you find implicit derivatives the same way you find ordinary derivatives, the only difference is that implicit derivatives have two variables in them.
So you take the derivative as usual and when you take the derivative of a y, you must put dy/dx behind it, because that is what you will be solving for.
This is where i get stuck, i know how to take the derivative, but when it comes to simplifying the derivatives and solving for dy/dx i get confused..
for example on the homework: on problem # 5
i took the derivative and got 3x^2-(x) (dy/dx) + (1) (y) + 2y dy/dx=0
from here i am confused on how to simplify the derivative and how to solve for dy/dx.. if someone can explain this to me it would help me to understand implicits better, Thanks :)
1. take the derivative of the function... then plug the x value they give you into the derivative and get the slope.
2. If they do not give you a y value, you have to plug the x value into the original function to get it.
3. After you have all the variables, you can set the equation up into the form y-y1=slope(x-x1).
Another thing i'm feeling better about is surprisingly optimization...
1. First things first, finding the primary and secondary functions are a must, your primary function will always be what they are asking for such as (maximize area, perimeter, etc.)
2. Once you find those, use your primary function to solve for one variable.
3. Once you find that variable, you plug it into its designated spot in the secondary function, then simplify.
4. Once that is done, take the derivative, set it equal to zero and solve for the remaining variable. One variable will be solved for.
5. Once you find the remaining variable, you plug it back into the equation where you solved for the first variable. Your other variable will be solved for.
Now lets get into the stuff we learned on Friday: implicit derivatives
Basically, you find implicit derivatives the same way you find ordinary derivatives, the only difference is that implicit derivatives have two variables in them.
So you take the derivative as usual and when you take the derivative of a y, you must put dy/dx behind it, because that is what you will be solving for.
This is where i get stuck, i know how to take the derivative, but when it comes to simplifying the derivatives and solving for dy/dx i get confused..
for example on the homework: on problem # 5
i took the derivative and got 3x^2-(x) (dy/dx) + (1) (y) + 2y dy/dx=0
from here i am confused on how to simplify the derivative and how to solve for dy/dx.. if someone can explain this to me it would help me to understand implicits better, Thanks :)
Post #9
Congrats to everyone! We've made it through our fist nine weeks and we're still..a little sane! ha
This past week was the ninth week of calculus, which means it was time for our first nine week exams. Monday and Tuesday we worked on our study guide and whoever had to finish their presentations went up and did them. Then Wednesday was the BIG DAY for the multiple choice part of our exams in calculus. Turns out that 'B-Rob' helped us by taking our best twenty! [Thank God, it defidently helped me!] Next was Thursday's Free Responce section of the exam...it consists of three questions: optimization, looking at a graph and telling the min/max, points of inflection, and concavity of either the derivative of that graph of the original of that graph, none the less we had one almost like that .. just without the graph, only the equation and that was our suprise! We also had to justify for the free responce, which i totally forgot, but I ended up going back and finishing the justification before the bell rang! I PASSED!
We began our second nine weeks Friday by learning Implicit Derivatives which involves x's and y's!
Here's your steps to follow when taking an Implicit Derivative:
1. Take the derivative [like normal] of both sides
2. Everytime you take the devivative of y state it by putting dy over dx or y prime
3. Solve for either dy over dx or y prime
Remember that if you want the slope you must plug in an x and a y value!....if you have an x but no a y [or opposite] plug into your orignal.
I think I understand this now...it's kinda tough for the big ones but..i'll get there!
Once again, CONGRATS to everyone making it through the first nine weeks!
This past week was the ninth week of calculus, which means it was time for our first nine week exams. Monday and Tuesday we worked on our study guide and whoever had to finish their presentations went up and did them. Then Wednesday was the BIG DAY for the multiple choice part of our exams in calculus. Turns out that 'B-Rob' helped us by taking our best twenty! [Thank God, it defidently helped me!] Next was Thursday's Free Responce section of the exam...it consists of three questions: optimization, looking at a graph and telling the min/max, points of inflection, and concavity of either the derivative of that graph of the original of that graph, none the less we had one almost like that .. just without the graph, only the equation and that was our suprise! We also had to justify for the free responce, which i totally forgot, but I ended up going back and finishing the justification before the bell rang! I PASSED!
We began our second nine weeks Friday by learning Implicit Derivatives which involves x's and y's!
Here's your steps to follow when taking an Implicit Derivative:
1. Take the derivative [like normal] of both sides
2. Everytime you take the devivative of y state it by putting dy over dx or y prime
3. Solve for either dy over dx or y prime
Remember that if you want the slope you must plug in an x and a y value!....if you have an x but no a y [or opposite] plug into your orignal.
I think I understand this now...it's kinda tough for the big ones but..i'll get there!
Once again, CONGRATS to everyone making it through the first nine weeks!
Wednesday, October 14, 2009
help!
can someone please explain to me how to do # 2 and # 3 on the optimization quiz we had? 3.7 homework quiz? pleaseeeeee :)
Tuesday, October 13, 2009
Exam Tomorrow
Okay, so this is probably too late, but anyway
Can anyone explain optimization to me! Tomorrow morning?...ish...maybe?
I've tried getting people to explain it but they either WON'T help me or CAN'T help me and since I missed today, I couldn't get B-Rob to help =/
I've been stressing all day..crying for the majority of the time....stressing some more...and I have finally decided that I don't care anymore. I've tried my hardest and that's that. =]
Also, these study guides are great for telling me that I have no idea what I'm doing on a lot of these and that I actually have somewhat of a clue on others...I LOVE MULTIPLE CHOICE! =] (no sarcasm)
Stay on the bright side kids.
If anyone else is terrified for this exam, reply with Aye :)
(BTW: Not meant to sound whiney, just venting...my gosh I needed that... and trying to figure out Optim.)
Can anyone explain optimization to me! Tomorrow morning?...ish...maybe?
I've tried getting people to explain it but they either WON'T help me or CAN'T help me and since I missed today, I couldn't get B-Rob to help =/
I've been stressing all day..crying for the majority of the time....stressing some more...and I have finally decided that I don't care anymore. I've tried my hardest and that's that. =]
Also, these study guides are great for telling me that I have no idea what I'm doing on a lot of these and that I actually have somewhat of a clue on others...I LOVE MULTIPLE CHOICE! =] (no sarcasm)
Stay on the bright side kids.
If anyone else is terrified for this exam, reply with Aye :)
(BTW: Not meant to sound whiney, just venting...my gosh I needed that... and trying to figure out Optim.)
Sunday, October 11, 2009
Post # 8
This week, since we did not go over anything new, I am going to show you how to use the Second Derivative Test to find all possible points of inflection and intervals of concavity. Remember, points of inflection only happen where there is a change of concavity.
Example: f'(x)= 6/(x^(2)+3)
First, you have to take the derivative of that, and you have to use the quotient rule, so the beginning of the problem will look like, [(x^(2)+3)(0)-6(2x)]/(x^(2)+3)^(2), which simplifies to -12x/(x^(2)+3)^2 remember, that was just the first derivative.
Second step is to take the derivative of the first derivative, that would make this step called taking the second derivative.
Once again u need to use the quotient rule, so f''(x)={(x2+3)^(2) -(12)-[(-12x)2(x^(2)+3)2x} all that over (x^(2)+3)^4 then you get a bunch of stuff, then you simplify, then you cancel, and if I typed all that up it would be ridiculous, so I'm just going to type the end answer of the second derivative. Which is, (3)(6)(x+1)(x-1) all over (x^(2)+3)^3
The possible points of inflection are found in the numerator of the finished second derivative, in this case, if you look, it would be x=1, and x=-1
so then you set up your points, (-infinity, -1) u (-1, 1) u (1, infinity)
then you plug in. f''(-2)= positive value f''(0)=negative value f''(2)=positive value
then you know that your intervals concave up @ (-infinity, -1) u (1,infinity) or x<1,>1
and it is concave down @ (-1,1) or -1
and you're points of inflection are x=-1, and x=1
okay, my question comes from a quiz that we had, it was the last problem and I didn't know how to do it, the problem goes like this: The sum of the perimeters of two squares is 24. Find the dimensions of the squares that produce the minimum total area.
I know it's a optimization problem, but I just don't know how to solve it. Help would be appreciated.
Example: f'(x)= 6/(x^(2)+3)
First, you have to take the derivative of that, and you have to use the quotient rule, so the beginning of the problem will look like, [(x^(2)+3)(0)-6(2x)]/(x^(2)+3)^(2), which simplifies to -12x/(x^(2)+3)^2 remember, that was just the first derivative.
Second step is to take the derivative of the first derivative, that would make this step called taking the second derivative.
Once again u need to use the quotient rule, so f''(x)={(x2+3)^(2) -(12)-[(-12x)2(x^(2)+3)2x} all that over (x^(2)+3)^4 then you get a bunch of stuff, then you simplify, then you cancel, and if I typed all that up it would be ridiculous, so I'm just going to type the end answer of the second derivative. Which is, (3)(6)(x+1)(x-1) all over (x^(2)+3)^3
The possible points of inflection are found in the numerator of the finished second derivative, in this case, if you look, it would be x=1, and x=-1
so then you set up your points, (-infinity, -1) u (-1, 1) u (1, infinity)
then you plug in. f''(-2)= positive value f''(0)=negative value f''(2)=positive value
then you know that your intervals concave up @ (-infinity, -1) u (1,infinity) or x<1,>1
and it is concave down @ (-1,1) or -1
and you're points of inflection are x=-1, and x=1
okay, my question comes from a quiz that we had, it was the last problem and I didn't know how to do it, the problem goes like this: The sum of the perimeters of two squares is 24. Find the dimensions of the squares that produce the minimum total area.
I know it's a optimization problem, but I just don't know how to solve it. Help would be appreciated.
post # eight
this week we reviewed.
Things that i do understand:
Tangent LIne- its simple. First step is to take a derivative, second plug in x value into that derivative, then you will get a slope. From there you take your slope and point and plug into the line formula.
Things that i dont understand.
I need more work with the limits and work with the optimization stuff. I get how to do optimizatin i know the steps i just always mess up getting the primary and/or secondary formula.
Things that i do understand:
Tangent LIne- its simple. First step is to take a derivative, second plug in x value into that derivative, then you will get a slope. From there you take your slope and point and plug into the line formula.
Things that i dont understand.
I need more work with the limits and work with the optimization stuff. I get how to do optimizatin i know the steps i just always mess up getting the primary and/or secondary formula.
posting..#8
This week in math we didn’t learn anything new we just did our presentations and our study packets for our test that’s on Wednesday. Although we didn’t learn anything new ill recap you on the steps of
Optimization
1 Identify primary and secondary equations your primary is the one your or maximizing or minimizing and your secondary is the other equation
2. Solve for your secondary variable and plug into your primary equation if your primary only has on variable this isn’t necessary
3. Plug into secondary equation to find the other value check your end points if necessary
Those are the steps of optimization hope that helped if you needed the recapped or you missed the notes.
What I need help on is Rolles theorem, mean value theorem and the intermediate value theorem. I don’t understand the first two but the intermediate value I can grasp I just would like a little help in remembering it.
But that’s it for me this week
Optimization
1 Identify primary and secondary equations your primary is the one your or maximizing or minimizing and your secondary is the other equation
2. Solve for your secondary variable and plug into your primary equation if your primary only has on variable this isn’t necessary
3. Plug into secondary equation to find the other value check your end points if necessary
Those are the steps of optimization hope that helped if you needed the recapped or you missed the notes.
What I need help on is Rolles theorem, mean value theorem and the intermediate value theorem. I don’t understand the first two but the intermediate value I can grasp I just would like a little help in remembering it.
But that’s it for me this week
Post 8
This week in calculus was pretty much a review week. We worked on the six review packets given to us for the exam. They helped me to understand some of the things I wasn't very clear on at the beginning of the nine weeks such as limits and tangent lines.
For limits, I was always so confused on how to figure out what the the limit was as it went to a certain number. I knew that one way to figure out the limit was to plug the number into x, but most of the time when I did this, the denominator of the limit would turn out to be zero, which left the limit undefined. I also knew that I could factor out my limit and maybe cross some things out, but sometimes this wouldn't work. This week I finally understood how to see what a certain limit is approaching using a table.
To see what the limit is approaching using a calculator, you use these steps:
1. Plug the limit equation into y= in your calculator
2. Go to your table function in your calculator and start plugging in values for the left and right of the number
3. When plugging in values, you will see the values will come very close to a particular number. This is your answer.
I also understood tangent lines. If an equation and an x value are given to you and the problem asks for a tangent line equation, you use these steps:
1. Plug the x value into your origional function to get your y value
2. Take the derivative of your function and plug your x value in to get your slope
3. Once you have an x value, a y value, and a slope, plug they all into point-slope form
I don't really have any questions this week except in need more help on my packets?
For limits, I was always so confused on how to figure out what the the limit was as it went to a certain number. I knew that one way to figure out the limit was to plug the number into x, but most of the time when I did this, the denominator of the limit would turn out to be zero, which left the limit undefined. I also knew that I could factor out my limit and maybe cross some things out, but sometimes this wouldn't work. This week I finally understood how to see what a certain limit is approaching using a table.
To see what the limit is approaching using a calculator, you use these steps:
1. Plug the limit equation into y= in your calculator
2. Go to your table function in your calculator and start plugging in values for the left and right of the number
3. When plugging in values, you will see the values will come very close to a particular number. This is your answer.
I also understood tangent lines. If an equation and an x value are given to you and the problem asks for a tangent line equation, you use these steps:
1. Plug the x value into your origional function to get your y value
2. Take the derivative of your function and plug your x value in to get your slope
3. Once you have an x value, a y value, and a slope, plug they all into point-slope form
I don't really have any questions this week except in need more help on my packets?
I'll just go over Instantaneous and average speed since no one seems to really have done that yet.
A wolf runs at y=93+2.3(t)^2 miles in t hours. What is it’s average speed during the first 5 seconds?
- State the slope formula: (y2-y1)/(x2-x1)
- Put the time you need to find into parenthesis or brackets: [0, 5] These are your two x’s.
- Plug x1 into your formula: y=93+2.3(0)^2 = 93 93 is your y1
- Plug x2 into your formula: y=93+2.3(5)^2=150.5 150.5 is your y2
- Plug back into your slope formula: (150.5-93)/(5-0)
- Simplify: 11.5 miles per hour
We can just use the same one for instantaneous speed.
- What is the instantaneous speed for t=3?
State the Instantaneous Speed formula:
Lim f(t-h)-f(t)
H->0 h - In the original problem, replace y with f(t): f(t)=93+2.3(t)2
- Plug in: Lim 93+2.3(3-h)^2-93+2.3(3)^2
H->0 h - Foil the parenthesis:
Lim 93+2.3(9-6h+h^2)-93+2.3(9)
H->0 h - Simplify:
Lim (93+20.7 –13.8h+2.3h^2) – (93 + 20.7)
H->0 h - Once you get it in it's simplest form, plug in for h.
Lim 2.3(0)+27.6
H->0 - ANSWER: 27.6 miles per hour.
For what i don't understand..i thought i understood limits, but idk what my deal is this week.
When it says is the limit of f(x) or f(2) larger.. what exactly am i doing.. i think
its one of the first questions on the ch. 1 study guide.
Post #8
Eight weeks down, many to go. This week in calculus, we presented and worked on our packets all week, so we really didn't learn anything new. I did learn that the table function on your calculator is a life saver and can be used to answer many problems.
To use your table function you have to plug in your equation to y equals and then press table which is second graph. If you are looking for the lim as it approaches -2, you will plug in numbers left to -2 and numbers right to -2.
Ex: -2-.1, -2-.01, -2-.001 for left and -2+.1, -2+.01, -2+.001 for the right side
You then have to see where each set of numbers are approaching to find the limit.
I also would like to remind everyone how to find rate of change because I had to learn it to complete chapter 3. To find the rate of change you have to plug into the formula f(b)-f(a)/b-a.
Ex: f(x) = x^3 + 9x on [1,3] and you are asked to find the average rate of change in f on [1,3].
f(3) = (3)^3 + 9(3) = 54
f(1) = (1)^3 + 9(1) = 10
54-10/ 3-1 = 44/2 = 22
One thing I am still confused on is how to find the formulas for optimization. I understand the steps once given the equations but I cannot figure out the formulas on my own.
I also do not understand b on number 9 chapter 3. I know y=125 but can't be 125 because it cannot exceed 100, so I do not know what to do next to get the correct answer.
To use your table function you have to plug in your equation to y equals and then press table which is second graph. If you are looking for the lim as it approaches -2, you will plug in numbers left to -2 and numbers right to -2.
Ex: -2-.1, -2-.01, -2-.001 for left and -2+.1, -2+.01, -2+.001 for the right side
You then have to see where each set of numbers are approaching to find the limit.
I also would like to remind everyone how to find rate of change because I had to learn it to complete chapter 3. To find the rate of change you have to plug into the formula f(b)-f(a)/b-a.
Ex: f(x) = x^3 + 9x on [1,3] and you are asked to find the average rate of change in f on [1,3].
f(3) = (3)^3 + 9(3) = 54
f(1) = (1)^3 + 9(1) = 10
54-10/ 3-1 = 44/2 = 22
One thing I am still confused on is how to find the formulas for optimization. I understand the steps once given the equations but I cannot figure out the formulas on my own.
I also do not understand b on number 9 chapter 3. I know y=125 but can't be 125 because it cannot exceed 100, so I do not know what to do next to get the correct answer.
post number 8
Wow, 8 weeks into the school year. sounds like a long time. this week was just reviewing for our exam which is in two parts on wednesday and thursday of this week, wednesday we are taking the multiple choice part of the exam. and on thursday we are taking the free response section, which mrs. robinson helped me abbey stephanie and trina with today at her house :) i would tell you what's on it, but you should've came to the study group.
ok, ill stop being mean now, and lets talk about calculus. at the study group today, i learned a lot about the process of elimination when it comes to multiple choice questions. also, if there is nothing else you can do with a problem that gives you a function and asks you to find something on a certain interval, like find the absolute extrema on the interval [0,2pi], then you can plug it into your calculator if you absolutely cannot figure it out by hand. also, short cuts are your friend :) like using the table function for problems like these. all of this really helped on the chap. 3 multiple choice part of our study guide.
some things i understand now are how to find a tangent line. the rules of finding a limit approaching infinity. how to take simple derivatives. instantaneous and average speed. all of these things. also how to look a a graph of a function and be able to know what the graph of the derivative of that function will look like, thank you dylan becnel :) haha. i also understand rolle's theorem and mean value theorem very well. what should i explain today? i think i'll explain how to look at the graph of a function and be able to know what the graph of the derivative of that function will look like.
Example:
let's say you are given the graph of a horizontal line. well, you know that the function has to look like this f(x)=#. like f(x)=3. and the horizontal line would be at 3. well the derivative of that would be 0. so the graph of the derivative of that function would be nothing. (chap. 3 multiple choice number 4)
the same thing i still don't understand every week. OPTIMIZATION. i hate it. i did learn today though that whenever you optimize a rectangle you will always end up with a square, which means whenever you work it out your x & y should be equal to the same thing. (chap. 3 multiple choice number 3) the x & y both ended up being equal to 11/2.
even though i got b rob to help me today with it, i still cannot do it by myself. any tips? just for optimization in general? please & thank you!
good luck on all of your exams tomorrow everyone :)
ok, ill stop being mean now, and lets talk about calculus. at the study group today, i learned a lot about the process of elimination when it comes to multiple choice questions. also, if there is nothing else you can do with a problem that gives you a function and asks you to find something on a certain interval, like find the absolute extrema on the interval [0,2pi], then you can plug it into your calculator if you absolutely cannot figure it out by hand. also, short cuts are your friend :) like using the table function for problems like these. all of this really helped on the chap. 3 multiple choice part of our study guide.
some things i understand now are how to find a tangent line. the rules of finding a limit approaching infinity. how to take simple derivatives. instantaneous and average speed. all of these things. also how to look a a graph of a function and be able to know what the graph of the derivative of that function will look like, thank you dylan becnel :) haha. i also understand rolle's theorem and mean value theorem very well. what should i explain today? i think i'll explain how to look at the graph of a function and be able to know what the graph of the derivative of that function will look like.
Example:
let's say you are given the graph of a horizontal line. well, you know that the function has to look like this f(x)=#. like f(x)=3. and the horizontal line would be at 3. well the derivative of that would be 0. so the graph of the derivative of that function would be nothing. (chap. 3 multiple choice number 4)
the same thing i still don't understand every week. OPTIMIZATION. i hate it. i did learn today though that whenever you optimize a rectangle you will always end up with a square, which means whenever you work it out your x & y should be equal to the same thing. (chap. 3 multiple choice number 3) the x & y both ended up being equal to 11/2.
even though i got b rob to help me today with it, i still cannot do it by myself. any tips? just for optimization in general? please & thank you!
good luck on all of your exams tomorrow everyone :)
Ash's 8th post
Okay, wow.....Yea
This week: powerpoint presentations and study guides...yipeee...fun *twirls finger nonenthusiastically*
Anyway, I pretty much wore out what I understood, so I can't really explain anything else. Also, I've been studying all weekend and I'm kinda like "duuuuuuuuuhhhhhhh *head hangs to side*" Yea, slightly braindead. Okay, but I will say this
I STILL DON'T GET OPTIMIZATION!!!! -.-
I feel like the stupid little kid that never understands how to spell the word 'cat' with a c not a k.
Also, those packets? I'm about to go cry...if that's what the exam looks like I KNOW I'm going to fail. I get half of it...the other half? Nope. Nada. Zip. Non. Zero.
Also, how is everyone studying for this exam? Doing the packet only? Doing the packet plus staring at your notes for 3 hours ineffectively? Nothing at all? I, for some reason, can't just study by doing the packet problems, or example problems, or just any kind of problems. I also can't study by staring at my notes. I need interaction. Think of me as a 2 year old...I won't get it if I stare at it....I need something to slowly state "That is a bike" over..and over...and over...and over...and over...and over...until I get it! -.-
Okay, I totally did not mean to whine...just merely type..and type..because I'm staring at the laptop screen as questions come to my head.....
*sigh* I guess I have to get off of the computer now and study for Calc, Chemistry, Ap Gov, Western Civ, English, AND the PSAT...by the way
For those of you who are taking the PSAT AND the Calc exam Wed...are you gonna ask your 7th hour teacher to move your exam? Maybe? Yes? No?
Okay..I'm done. I apologize for making you sit here and lose about 45 brain cells.
This week: powerpoint presentations and study guides...yipeee...fun *twirls finger nonenthusiastically*
Anyway, I pretty much wore out what I understood, so I can't really explain anything else. Also, I've been studying all weekend and I'm kinda like "duuuuuuuuuhhhhhhh *head hangs to side*" Yea, slightly braindead. Okay, but I will say this
I STILL DON'T GET OPTIMIZATION!!!! -.-
I feel like the stupid little kid that never understands how to spell the word 'cat' with a c not a k.
Also, those packets? I'm about to go cry...if that's what the exam looks like I KNOW I'm going to fail. I get half of it...the other half? Nope. Nada. Zip. Non. Zero.
Also, how is everyone studying for this exam? Doing the packet only? Doing the packet plus staring at your notes for 3 hours ineffectively? Nothing at all? I, for some reason, can't just study by doing the packet problems, or example problems, or just any kind of problems. I also can't study by staring at my notes. I need interaction. Think of me as a 2 year old...I won't get it if I stare at it....I need something to slowly state "That is a bike" over..and over...and over...and over...and over...and over...until I get it! -.-
Okay, I totally did not mean to whine...just merely type..and type..because I'm staring at the laptop screen as questions come to my head.....
*sigh* I guess I have to get off of the computer now and study for Calc, Chemistry, Ap Gov, Western Civ, English, AND the PSAT...by the way
For those of you who are taking the PSAT AND the Calc exam Wed...are you gonna ask your 7th hour teacher to move your exam? Maybe? Yes? No?
Okay..I'm done. I apologize for making you sit here and lose about 45 brain cells.
Post Number Eight
soooo week number eight has come to a close and calculus still seems to stress me out daily.
oh well :)
This past week we reviewed for our exams and presented our power point presentations. I felt like i learned a lot about different jobs and how much math does play a part in everyday life. But onto the real stuff.
Some things i'm finally catching on to:
oh well :)
This past week we reviewed for our exams and presented our power point presentations. I felt like i learned a lot about different jobs and how much math does play a part in everyday life. But onto the real stuff.
Some things i'm finally catching on to:
- Tangent lines
- Derivatives in general (finallyyyyyyyyy)
- Limits (sometimes)
Of course i'm still not getting some things also:
- Optimization- i understand the steps and all so don't comment me telling me them. I just can't find the two formulas at the beginning. If anyone has any ideas or can help me with this I NEEED IT
- Looking at graphs determining derivatives and such
- Vertical asymptotes
- And of course the easy stuff that i always seem to mess up on that we will not speak of
So now that that was said i'll give an example of something i understand :)
g(x)=x^2 - 4x + 9
Write the equation of the tangent line to the graph of g at x=3.
First you can simply just find the y value so you can later put your information in point slope form. Since you are given the x value at x=3, you just plug it into the original formula to find the y.
g(3)=3^2 - 4(3) + 9
g(3)=6
So your point is (3, 6)
Now you need a slope, so guess what we do now.
Take a derivative, which is what we'll be doing everyday for what feels like the rest of our lives so do ittttt!
g'(x)=2x-4
Now plug in the x value into the derivative.
g'(3)=2(3) - 4
g'(3)=2
Now that you have a point and a slope, you put it into point-slope form because it is asking for an equation of the tangent line.
Your final answer will be y - 6=2(x - 3)
Easy enough, right?
Oh and another thing i learned this week is how to use the table function and that you should treat it like your bible basically (Thanks John!)
If anyone can help me with anything please let me know. I'm always struggling with something. But thanks to all of these study guides i think i'm finally getting a hang of some of these things.
Now for yet another week of Calculus
Post #8
It has been eight weeks already...wow. Anyways this week was review, review, and review for our exam.
First of all, I realized that multiple choice is my best friend because of eliminating. Also, always plug in to your calculator if everyting else fails. And both of those things really helped with the chapter 3 packet.
So the things that are finally clicking in my head:
1. The limit does exist at a removable (thanks John).
2. When it gives you the graph of f and you are suppose to find the graph of the derivative of f. (like #4 on chapter 3 m/c pakcet)
3. And to make sure my calculator is in radians when needed.
Now for some example problems I can actually work:
1. Find the value of c guaranteed by the INtermediate Value Theorem. f(x)=x^2-2x-3,[4,8], f(c)=12. And the choices are A) 3 B) 2 C) 5 D) 7 E) 6
All you do is plug in each choice for your x and which ever one gives you 12 is your answer. f(x)=x^2-2x-3 =5^2-2(5)-3 =12 So, the answer is C) 5.
2. Find the limit. lim sinx when x-->pi/4
This is real simple, just plug in. sin(pi/4)= squareroot of 2/2
For stuff I don't know:
1. I'm still ify with finding primary and secondary equations for optimization.
2. Also, chapter one stuff with limits, for some reason I still cannot do grasp limits. Can anyone look at that packet explain to me how to do #2, part b?
3. And what is the derivative of tan^8x? Do I bring the 8 to the front?
4. (#9 on chapter 2) Find the slope of the graph of the function at the give value. f(x)=2x^2+4x-6/x^2 when x=5 The answer is suppose to be -3012/125. I can get the bottom number, but for some reason I can't get the top number. I might be doing the derivative wrong. Someone help?
Hope someone can help me! Well I guess it's back to studying for my other exams :(
First of all, I realized that multiple choice is my best friend because of eliminating. Also, always plug in to your calculator if everyting else fails. And both of those things really helped with the chapter 3 packet.
So the things that are finally clicking in my head:
1. The limit does exist at a removable (thanks John).
2. When it gives you the graph of f and you are suppose to find the graph of the derivative of f. (like #4 on chapter 3 m/c pakcet)
3. And to make sure my calculator is in radians when needed.
Now for some example problems I can actually work:
1. Find the value of c guaranteed by the INtermediate Value Theorem. f(x)=x^2-2x-3,[4,8], f(c)=12. And the choices are A) 3 B) 2 C) 5 D) 7 E) 6
All you do is plug in each choice for your x and which ever one gives you 12 is your answer. f(x)=x^2-2x-3 =5^2-2(5)-3 =12 So, the answer is C) 5.
2. Find the limit. lim sinx when x-->pi/4
This is real simple, just plug in. sin(pi/4)= squareroot of 2/2
For stuff I don't know:
1. I'm still ify with finding primary and secondary equations for optimization.
2. Also, chapter one stuff with limits, for some reason I still cannot do grasp limits. Can anyone look at that packet explain to me how to do #2, part b?
3. And what is the derivative of tan^8x? Do I bring the 8 to the front?
4. (#9 on chapter 2) Find the slope of the graph of the function at the give value. f(x)=2x^2+4x-6/x^2 when x=5 The answer is suppose to be -3012/125. I can get the bottom number, but for some reason I can't get the top number. I might be doing the derivative wrong. Someone help?
Hope someone can help me! Well I guess it's back to studying for my other exams :(
post 8
So this week in calculus it was a mixture between power point presentations and working on our study guides. One thing I understand in our study guide is tangent lines. All you do is take the derivative of the equation. Then plug in the x value from the point given giving you the slope. Next plug the slope and point in to slope intercept form which is y-y1=slope(x-x1). Also I understand some limit stuff. To find the vertical asymtote just set the bottom equal to 0. Also I understand how to take derivatives. Whether it be the easy ones where its just an equation, to product rule, or quotient rule. All the work and practice we did on it helped me out a lot and now I completely understand how to take the derivative of many equations.
But I still do not fully understand optimization. I just can not seem to get it fully at all. Also I do not really remember the Intermediate Value Theorem. I probably know how to do it I just need a refreshement. So if anyone can help me with either of these it would be great.
Week #8
On Monday, Tuesday, and Friday this week, we did our power point presentations on jobs using math. But, we worked on our exam review packets pretty much everyday.
Let's start off with something I do not understand in the packets:
Intermediate Value Theorem. Example: the first question of one of the multiple choice packets.
I don't even know how to start the problem.
Something I do understand:
tangent line:
example: the first problem on another MC packet.
take the derivative, plug in x-value, get slope, set up line equation.
Well, back to studying for Calculus/Chemistry/English/AP Gov't./PSAT
Let's start off with something I do not understand in the packets:
Intermediate Value Theorem. Example: the first question of one of the multiple choice packets.
I don't even know how to start the problem.
Something I do understand:
tangent line:
example: the first problem on another MC packet.
take the derivative, plug in x-value, get slope, set up line equation.
Well, back to studying for Calculus/Chemistry/English/AP Gov't./PSAT
Post #8
This week we reviewed and did packets...
so here i go on things i now understand.
Soo, optimization..
a. identify primary and secondary
(primary the one your maximizing or minimizing)(secodary the other one)
b. solve secondary for 1 variable and plug into primary
c.take derivative. plug into secondary equation.
I also now understand how to figure out different types of limits. You find vertical asymptotes when you set the bottom of a fraction equal to zero and solve. For horizontal asymptotes, you use the three rules when looking at the degree on the top of the fraction and on the bottom. Anything you can cancel from a function is a removable. Another thing i understand better is how to use the first and second derivative test. When using the first derivative test, you take the derivative of the function and set it equal to zero and solve for x. Then you set up your x values into intervals to see which ones are max and mins etc. When using the second derivative test, you take the derivative of a function two times and set equal to zero and solve for x. You put these x values into intervals as well to find if a graph is concave up or down, point of inflection, etc.
The thing i still do not understand is simplifying. I get stuck when there is nothing left to factor out..can anyone tell me what to do after?
so here i go on things i now understand.
Soo, optimization..
a. identify primary and secondary
(primary the one your maximizing or minimizing)(secodary the other one)
b. solve secondary for 1 variable and plug into primary
c.take derivative. plug into secondary equation.
I also now understand how to figure out different types of limits. You find vertical asymptotes when you set the bottom of a fraction equal to zero and solve. For horizontal asymptotes, you use the three rules when looking at the degree on the top of the fraction and on the bottom. Anything you can cancel from a function is a removable. Another thing i understand better is how to use the first and second derivative test. When using the first derivative test, you take the derivative of the function and set it equal to zero and solve for x. Then you set up your x values into intervals to see which ones are max and mins etc. When using the second derivative test, you take the derivative of a function two times and set equal to zero and solve for x. You put these x values into intervals as well to find if a graph is concave up or down, point of inflection, etc.
The thing i still do not understand is simplifying. I get stuck when there is nothing left to factor out..can anyone tell me what to do after?
8th post
This week in calculus we worked on exam review packets. We have 6 of them, three are multiple choice and three are free response. I am getting much better at the multiple choice questions, especially when they ask you to find a limit when you are given a graph. I also understand how to find left and right hand limits better:
when they ask you to find the lefthand limit of 3. you cover up the right side of the graph and see when the line is approaching on the y axis on the left side. When they ask you to find the righthand limit of 3, you cover up the left hand side of the graph and see what y value the line is approaching on the right side. After finding those two, if you are asked to find the limit of 3. If the y values are not the same the limit does not exist, if they are the same then the limit does exist. Also by studying i have a better grasp on the first and second derivative test. Understanding those test better have helped me on a lot of the multiple choice questions i did not understand how to do earlier in the week. On the free response sheets, i understand how to do more limit problems. When they ask what limit is greater lim x approaches 1 or f(2). you look at the functions they give you. One is x=1 and the answer is 3. So by x=1 the limit is 3. Then there is a function 2 is less than or equal to x. So you plug f(2) into that function and the limit is x-1 which gives you 1. There fore as x approaches 1 is bigger than f(2).
The only thing i am still having problems with is some optimization problems. I understand now how to find primary and secondary functions but sometimes i get stuck in actually doing the problem. If someone can lists some easy steps on how to do optimization it would help a lot. Thanks :)
when they ask you to find the lefthand limit of 3. you cover up the right side of the graph and see when the line is approaching on the y axis on the left side. When they ask you to find the righthand limit of 3, you cover up the left hand side of the graph and see what y value the line is approaching on the right side. After finding those two, if you are asked to find the limit of 3. If the y values are not the same the limit does not exist, if they are the same then the limit does exist. Also by studying i have a better grasp on the first and second derivative test. Understanding those test better have helped me on a lot of the multiple choice questions i did not understand how to do earlier in the week. On the free response sheets, i understand how to do more limit problems. When they ask what limit is greater lim x approaches 1 or f(2). you look at the functions they give you. One is x=1 and the answer is 3. So by x=1 the limit is 3. Then there is a function 2 is less than or equal to x. So you plug f(2) into that function and the limit is x-1 which gives you 1. There fore as x approaches 1 is bigger than f(2).
The only thing i am still having problems with is some optimization problems. I understand now how to find primary and secondary functions but sometimes i get stuck in actually doing the problem. If someone can lists some easy steps on how to do optimization it would help a lot. Thanks :)
post 8
this week we reviewed for our exam. we had a million packets we had to do adn it was pretty stressful. i know how to optimize pretty well. ( i did pretty good on that quiz :). Optimization is solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a scalar, real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.
taking a derivative is easy. i know all the formulas used for taking the derivative.
Rolle's theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero.
the mean value theorem: states that given a section of a smooth (differentiable) curve, there is at least one point on that section at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the section.[1] It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.
im having problems w/ the little things in all these these formulas and theorems like i forget something and then i mess up the entire problem so other than forgetting little things here and there im doin alright.
taking a derivative is easy. i know all the formulas used for taking the derivative.
Rolle's theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero.
the mean value theorem: states that given a section of a smooth (differentiable) curve, there is at least one point on that section at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the section.[1] It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.
im having problems w/ the little things in all these these formulas and theorems like i forget something and then i mess up the entire problem so other than forgetting little things here and there im doin alright.
8th post
this week was about reviewing and doing a billion packets.......
review:
The derivative:
of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.
optimazation:
In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a scalar, real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.
Rolle's theorem:
essentially states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero.
the mean value theorem:
states, roughly, that given a section of a smooth (differentiable) curve, there is at least one point on that section at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the section.[1] It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.
okay so im still having problems with optimazation so if anyone can put examples up that would be helpful.
review:
The derivative:
of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.
optimazation:
In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a scalar, real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.
Rolle's theorem:
essentially states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero.
the mean value theorem:
states, roughly, that given a section of a smooth (differentiable) curve, there is at least one point on that section at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the section.[1] It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.
okay so im still having problems with optimazation so if anyone can put examples up that would be helpful.
Post #8
This week in Calculus we reviewed for the exam. We have 6 packets as our study guide for the exam so this week we worked on that. We also had our nine weeks project which was to find a job that requires math. I did my project on Geomatics Engineers. I learned that they have more science than math, however they need advanced math and calculus in order to do their job. Throughout the week we all presented our projects and worked on the exam study guide.
As a review:
know how to take a derivative!
know how to do the first derivative test!
know your limits from last year!!!
know how to do the second derivative test!
know the vocab in order to justify nicely and know what you have to do in the problem
know optimization
know mean value, intermediate, and rolle's theroms! [and how do use them]
know average speed or velocity as well as the insintanious speed!
THE EXAM IS ON THURSDAY SO STUDY STUDY STUDY!!!
i still don't quite understand all of the vocab..so when i'm looking at a problem i'm not sure what it's asking me to do...i'll have to study that!!
~ElliE~
As a review:
know how to take a derivative!
know how to do the first derivative test!
know your limits from last year!!!
know how to do the second derivative test!
know the vocab in order to justify nicely and know what you have to do in the problem
know optimization
know mean value, intermediate, and rolle's theroms! [and how do use them]
know average speed or velocity as well as the insintanious speed!
THE EXAM IS ON THURSDAY SO STUDY STUDY STUDY!!!
i still don't quite understand all of the vocab..so when i'm looking at a problem i'm not sure what it's asking me to do...i'll have to study that!!
~ElliE~
Post 8
Ok...I have no idea if we're supposed to be doing this since we're studying for the exam, or what? But while I'm on here, I would like to say that I am getting awesome at multiple choice questions, and free responses are coming along. Also, I have finally grasped the concept of limits fully! (jumps for joy) What'd you know?! The only thing I'm having problems with is these graph things that keep popping up in multiple choice. Like, if someone could explain number 32 on the packet beginning with the intermediate value theorem, it would be greatly appreciated. Muchas gracias.
Sorry for the mini-blog thing, but seeing as John is the only one who did this, IDK? I'm going back to do my packets now/english essay.
Sorry for the mini-blog thing, but seeing as John is the only one who did this, IDK? I'm going back to do my packets now/english essay.
Week 8
Calculus Week #8 A.K.A. Exam Study Week. :-)
So this week was all about doing more and more practice for exams, as well as presenting our 9-weeks projects.
As we get closer and closer to our exams, I'm getting better at doing multiple choice Calculus questions. They are coming so easily to me now. Derivatives are also getting really really easy, and if it doesn't come out just right, I can usually find my error quickly. We got 6 different packets, 1 for each chapter of 1-3, multiple choice and free response. As of writing this post, I have done all of the multiple choice as well as chapter 1 free response. On the multiple choice I got about 5-7 wrong out of all 3 packets and they were all silly mistakes so I think I'm good on those. And as far as free response, we'll get those answers on Monday and if I have any questions, I'll post them here.
As far as explaining something... I want to point this out for once and for all
THE LIMIT EXISTS AT A REMOVEABLE...stop thinking it doesn't.
Okay. Done that :-)
Good luck to everyone on exams.
-John
So this week was all about doing more and more practice for exams, as well as presenting our 9-weeks projects.
As we get closer and closer to our exams, I'm getting better at doing multiple choice Calculus questions. They are coming so easily to me now. Derivatives are also getting really really easy, and if it doesn't come out just right, I can usually find my error quickly. We got 6 different packets, 1 for each chapter of 1-3, multiple choice and free response. As of writing this post, I have done all of the multiple choice as well as chapter 1 free response. On the multiple choice I got about 5-7 wrong out of all 3 packets and they were all silly mistakes so I think I'm good on those. And as far as free response, we'll get those answers on Monday and if I have any questions, I'll post them here.
As far as explaining something... I want to point this out for once and for all
THE LIMIT EXISTS AT A REMOVEABLE...stop thinking it doesn't.
Okay. Done that :-)
Good luck to everyone on exams.
-John
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