Also as I said in class... blogs are cumulative. You must write a minimum of 250 words. If you didn't understand something from this week then you can reference past material. The idea is that you are looking through your notes once a week and asking questions on things you find you don't understand and explaining something you do. You should not repost my notes. It should be in your own words. You should not summarize the week or complain. If you are having trouble getting the word count work an example problem along with your explanation. NOT the one that I did but one from homework or somewhere else. Especially since there is a quiz on Monday I would expect that there will be plenty of questions as people go through their notes from the whole year and plenty of explanations from the topics throughout the year so far.
Saturday, September 12, 2009
To Clarify
For everyone that was absent on Thurs. Friday was NOT a continuation. It was new for everyone. Thurs we continued to work with the first derivative test, went over differentiability (which does not pertain to Friday's notes) and worked on justifications. The homework was not based on Friday's notes. None of the problems ask you for concavity. It has to do with the first derivative test. However, you have to justify all of your answers. This is so I can get an idea and give you pointers on your justifications NOW so that you don't fail the test on Thurs.
Post #4
So, it was the fouth week of calculus and it was just as bad as the second for me. I'm not sure why, maybe it's because we didn't have school Monday, and Mrs. Robinson wasn't there Tuesday and Wednesday, then I went to Tulane all day on Thursday, so I basically only had one day, which was Friday, to really learn something, BUT...I was lost!
So, Tuesday and Wednesday wasn't bad at all...I thought I knew was I was doing. The worksheet wasn't bad and the vocabulary didn't seem hard to understand and write in my own words either. Then Thursday came, I went to Tulane because I was chosen out of the Senior class to tour the school we could most likely have an opportunity to attend one day. I ended up having to miss class, WHICH SUCKS btw, making it really hard to understand what we did Friday.
Friday, I'm guessing that we "continued" to learn what Mrs. Robinson taught on Thursday. We did learn the Second Derivative Test. There are points of inflection, intervals of concavity [concave up/concave down], and shortcut for MAX & MIN. She said, "Beware, points of inflection only happen if there is a change in concavity." An example problem would be:
x^2 + 1
----------
x^2 - 4
since that's the original, we need to first find the first derivative:
(x^2 - 4) (2x) - (x^2+1) (2x)
------------------------------------
(x^2-4)^2 which gives you...
-10x
-------------
(x^2-4)^2 for the first derivative....now we have to take another derivative from this in order to find the second derivative...
(x^2)^2 (-10) -- [(-10x)2(x^2-4)(2x)]
-----------------------------------------------
(x^2-4)^4 giving you....
-30x^2+40
---------------
(x^2-4)^3 which, simplified, will give you...
10(3x^2+4)
----------------
(x^2-4)^3 for the second derivative!!
your points of discontinuity is plus or minus 2 [from your original...take the bottom and set equal to zero and solve]. which means from (-infinity, -2) it's concave up, from (-2,2) it's concave down, from (2,+infinity) it's concave up. Another way of writing it is....concave up: x<-2 x>2......concave down: -2
To be honest...I really don't understand this. First off, taking the derivative...I always get something mixed up so I get it wrong, screwing my whole problem up. I wish there were simple terms to put it in, in order to make me understand, but I just can't get it. I know the formulas, so I'm not sure what I'm doing wrong, probably simple algebra...which btw isn't so simple!! Second, once I get the derivative of the first, the second derivative...which is like the same way...is just harder to do :(
But I do understand when it's concave up and down and all the rest of those vocabulary words. Oh but wait, how do you get that if you have just a problem...like on the homework...number 9...
1
----
x^2 it says to identify the open intervals on which the function is increasing or decreasing. So do I just take the derivative and find the points of discontinuity, then plug into the original...so see if it's increasing or decreasing...and since it's increasing/decreasing..isn't it just .. I only have to take the first derivative?
I'm pretty lost, and I don't like this...I try to ask questions in class, and it just doesn't seem to work or help!
--Ellie
So, Tuesday and Wednesday wasn't bad at all...I thought I knew was I was doing. The worksheet wasn't bad and the vocabulary didn't seem hard to understand and write in my own words either. Then Thursday came, I went to Tulane because I was chosen out of the Senior class to tour the school we could most likely have an opportunity to attend one day. I ended up having to miss class, WHICH SUCKS btw, making it really hard to understand what we did Friday.
Friday, I'm guessing that we "continued" to learn what Mrs. Robinson taught on Thursday. We did learn the Second Derivative Test. There are points of inflection, intervals of concavity [concave up/concave down], and shortcut for MAX & MIN. She said, "Beware, points of inflection only happen if there is a change in concavity." An example problem would be:
x^2 + 1
----------
x^2 - 4
since that's the original, we need to first find the first derivative:
(x^2 - 4) (2x) - (x^2+1) (2x)
------------------------------------
(x^2-4)^2 which gives you...
-10x
-------------
(x^2-4)^2 for the first derivative....now we have to take another derivative from this in order to find the second derivative...
(x^2)^2 (-10) -- [(-10x)2(x^2-4)(2x)]
-----------------------------------------------
(x^2-4)^4 giving you....
-30x^2+40
---------------
(x^2-4)^3 which, simplified, will give you...
10(3x^2+4)
----------------
(x^2-4)^3 for the second derivative!!
your points of discontinuity is plus or minus 2 [from your original...take the bottom and set equal to zero and solve]. which means from (-infinity, -2) it's concave up, from (-2,2) it's concave down, from (2,+infinity) it's concave up. Another way of writing it is....concave up: x<-2 x>2......concave down: -2
To be honest...I really don't understand this. First off, taking the derivative...I always get something mixed up so I get it wrong, screwing my whole problem up. I wish there were simple terms to put it in, in order to make me understand, but I just can't get it. I know the formulas, so I'm not sure what I'm doing wrong, probably simple algebra...which btw isn't so simple!! Second, once I get the derivative of the first, the second derivative...which is like the same way...is just harder to do :(
But I do understand when it's concave up and down and all the rest of those vocabulary words. Oh but wait, how do you get that if you have just a problem...like on the homework...number 9...
1
----
x^2 it says to identify the open intervals on which the function is increasing or decreasing. So do I just take the derivative and find the points of discontinuity, then plug into the original...so see if it's increasing or decreasing...and since it's increasing/decreasing..isn't it just .. I only have to take the first derivative?
I'm pretty lost, and I don't like this...I try to ask questions in class, and it just doesn't seem to work or help!
--Ellie
Friday, September 11, 2009
Ash's 4th post
Okay, so i have a problem.
Mrs. Robinson wasn't at school Tuesday or Wednesday, I wasn't at school yesterday, and today was a continuation of yesterday.
I didn't understand what was going on today, not only because I felt horrible and couldn't focus, but because I had no idea what was going on in general. I don't think I can write 300 words on something that I have no clue about anyway.
So, can someone explain what happened Thursday and Friday? I don't mean on here...that would be too long, but sometime Monday maybe? Thanks :):)
Mrs. Robinson wasn't at school Tuesday or Wednesday, I wasn't at school yesterday, and today was a continuation of yesterday.
I didn't understand what was going on today, not only because I felt horrible and couldn't focus, but because I had no idea what was going on in general. I don't think I can write 300 words on something that I have no clue about anyway.
So, can someone explain what happened Thursday and Friday? I don't mean on here...that would be too long, but sometime Monday maybe? Thanks :):)
Wednesday, September 9, 2009
comments..
So if I can't answer anyone's questions am I in trouble? Everyone asked questions on what I said I don't understand...
Okay...so...
What do we do if I don't see really any questions to answer? I feel that it's quite retarded to answer a question that's already been answered...so...what should I do in order to get my two comments?
Monday, September 7, 2009
Post #2
Ok. So the beginning of the week was hectic in terms of preparing for the test and such. Going into the test, I thought that I was doing good. I knew all of my derivative formulas and could work out problems to the best of my ability, I think. However, even though I knew that limits would be on the test, I was not nearly prepared as I thought I was for that portion. I understand how to find finite and infinite limits, but I totally do not remember how to do the right and left hand limits (that would be my major question ???).
On Thursday when Ms. Robinson introduced to us all the of the vocabulary for the graphs, I was a little freaked out. I kept copying down all the stuff on the graphs, but couldn't really grasp it, that is, until Friday.
So, I after doing all the examples I finally got it, and the grouping of the terms kind of helped me as well. This is the way I remember it:
Original: Increasing, Decreasing, maximum, minimum.
1st derivative: Positive slope, Negative slope, horizontal tangent
2nd derivative: Concave up, Concave down, point of inflection.
And then we have how they're all related:
(Increasing, Negative slope, Derivative below the axis, concave up.)
(Decreasing, Positive slope, Derivative above the axis, concave down.)
(Zero of a derivative, Horizontal tangent, minimum.)
For me, I had to see the graph to do this at first, but then on Friday we also went into doing the first derivative tes (KEEP IN MIND: FIRST derivative).
Steps are as follows:
1. Take the derivative
2. Set = 0
3. Solve or x =>max & min (extrema), horiz tangent
4. Set up intervals using step 3
5. plug in 1st derivative
6. To find an absolute max/min plug values from #5 into original function. Check endpoints.
So, that's all I have and if someone could review the whole right left hand thing for me, it would be greatly appreciated!
On Thursday when Ms. Robinson introduced to us all the of the vocabulary for the graphs, I was a little freaked out. I kept copying down all the stuff on the graphs, but couldn't really grasp it, that is, until Friday.
So, I after doing all the examples I finally got it, and the grouping of the terms kind of helped me as well. This is the way I remember it:
Original: Increasing, Decreasing, maximum, minimum.
1st derivative: Positive slope, Negative slope, horizontal tangent
2nd derivative: Concave up, Concave down, point of inflection.
And then we have how they're all related:
(Increasing, Negative slope, Derivative below the axis, concave up.)
(Decreasing, Positive slope, Derivative above the axis, concave down.)
(Zero of a derivative, Horizontal tangent, minimum.)
For me, I had to see the graph to do this at first, but then on Friday we also went into doing the first derivative tes (KEEP IN MIND: FIRST derivative).
Steps are as follows:
1. Take the derivative
2. Set = 0
3. Solve or x =>max & min (extrema), horiz tangent
4. Set up intervals using step 3
5. plug in 1st derivative
6. To find an absolute max/min plug values from #5 into original function. Check endpoints.
So, that's all I have and if someone could review the whole right left hand thing for me, it would be greatly appreciated!
Post 3
So far this week we've only really learned two new things. We learned how to take the first and second derivative from a graph, and we also learned how to find a first derivative by using the first derivative test.
Along with learning the first and second derivatives, we've learned the vocabulary associated with the graphs. We learned that the words increasing, decreasing, and minimum and maximum are related to the origional graph; positive slope, negative slope, and horizontal tangent are related to the first derivative; concave up and concave down are related to the second derivative. We learned that when there's a positive slope and the graph concaves up, the derivative will be above the axis, that if a slope is negative and it concaves down the derivative will be below the axis, and if a derivative has a zero, it will form a horizontal tangent and a point of inflection.
To find the first derivative, there are steps to follow:
1. take a derivative
2. set it equal to zero
3. solve for x giving you either max, min, horizontal tangents, extrema, or critical points
4. set up intervals using step 3
5. plug in first derivative
6. to find an absolute max/min, plug values from step 5 into the origional function and check end points
7. remember to check for all points of continuity
If the question would ask you either where the graph is increasing or decreasing, or where the horizontal tangent or min and max are, you would stop at step number 3 and be finished with the problem. If the problem would as you something like "Find the relative max and min" you would bo on to steps 4 through 7 setting up your intervals and plugging values into the first derivative and the origional function.
The only real problem I had this week was looking at the graphs and trying to decide how to get the first and second derivatives out of them. I just get lost from the beginning looking at the graphs. I think if I have more practice on the graphs I'll do fine.
Along with learning the first and second derivatives, we've learned the vocabulary associated with the graphs. We learned that the words increasing, decreasing, and minimum and maximum are related to the origional graph; positive slope, negative slope, and horizontal tangent are related to the first derivative; concave up and concave down are related to the second derivative. We learned that when there's a positive slope and the graph concaves up, the derivative will be above the axis, that if a slope is negative and it concaves down the derivative will be below the axis, and if a derivative has a zero, it will form a horizontal tangent and a point of inflection.
To find the first derivative, there are steps to follow:
1. take a derivative
2. set it equal to zero
3. solve for x giving you either max, min, horizontal tangents, extrema, or critical points
4. set up intervals using step 3
5. plug in first derivative
6. to find an absolute max/min, plug values from step 5 into the origional function and check end points
7. remember to check for all points of continuity
If the question would ask you either where the graph is increasing or decreasing, or where the horizontal tangent or min and max are, you would stop at step number 3 and be finished with the problem. If the problem would as you something like "Find the relative max and min" you would bo on to steps 4 through 7 setting up your intervals and plugging values into the first derivative and the origional function.
The only real problem I had this week was looking at the graphs and trying to decide how to get the first and second derivatives out of them. I just get lost from the beginning looking at the graphs. I think if I have more practice on the graphs I'll do fine.
okayyy, so calculus.
the first part of the week was stressful because we were getting ready for
the test, but after that i was alright. we reviewed infinite and finite
limits that we did at the end of last year in advanced math. thankfully that's
one concept i understand.
the limit rules are stuck in my headd.
if the degree on the top=degree on bottom the limit is the coefficients.
if the degree on the top is greater that the degree on the bottom the
limit is plus/minus infiniti
and if the degree on the top is less than the degree on the bottom the
limit is 0.
--horizontal asymptotes were also easy to remember.
the days after the test we learned on brandi's handy dandy projector.
..the first day we got our definitions, which are all easy to understand, especially
after hearing kaitlyn repeat them over and over and over again =)
as far as figureing out the derivatives goes, i was confused for quite a while.
i get the whole.. if the slope is positive, it's increasing and if the slope is negative, it's decreasing concept and the difference between concaved up and concaved down but i just don't know where to begin deciphering between derivatives and i forget to set up intervals.
the first part of the week was stressful because we were getting ready for
the test, but after that i was alright. we reviewed infinite and finite
limits that we did at the end of last year in advanced math. thankfully that's
one concept i understand.
the limit rules are stuck in my headd.
if the degree on the top=degree on bottom the limit is the coefficients.
if the degree on the top is greater that the degree on the bottom the
limit is plus/minus infiniti
and if the degree on the top is less than the degree on the bottom the
limit is 0.
--horizontal asymptotes were also easy to remember.
the days after the test we learned on brandi's handy dandy projector.
..the first day we got our definitions, which are all easy to understand, especially
after hearing kaitlyn repeat them over and over and over again =)
as far as figureing out the derivatives goes, i was confused for quite a while.
i get the whole.. if the slope is positive, it's increasing and if the slope is negative, it's decreasing concept and the difference between concaved up and concaved down but i just don't know where to begin deciphering between derivatives and i forget to set up intervals.
post 3
we learned many things this past week that i've picked up on pretty well. The first derivative test gave me some trouble but im getting the hang of that. andthe vocab of the graphs are easy. which is Increasing-slope going up; original, Decreasing-slope going down; original, Positive Slope- first derivative which is above, Negative Slope- first derivative which is below, Concave Up which means second derivative, Concave down which also means 2nd derivative, Horizontal Tangent the slope equals zero, Derivative above axis, Derivative below axis, Zero of derivative
Maximum-original, Minimum-orignial, Extrema. When the slope of a graph is positive the graph is moving from right to left and it is going up, which means it is increasing. when the slope of a graph is negative it is going from left to right and it is descending which makes it decrease. I've maintained the knowledge of all the derivative formulas even though we just were using em like a few days ago. the only thing i dont really remember all too well is the derivative test. i can't rreally remember all the steps w/out my notebook. if anyone knows any tricks to remembering the the derivative tests' rules that would be pretty helpful.
Maximum-original, Minimum-orignial, Extrema. When the slope of a graph is positive the graph is moving from right to left and it is going up, which means it is increasing. when the slope of a graph is negative it is going from left to right and it is descending which makes it decrease. I've maintained the knowledge of all the derivative formulas even though we just were using em like a few days ago. the only thing i dont really remember all too well is the derivative test. i can't rreally remember all the steps w/out my notebook. if anyone knows any tricks to remembering the the derivative tests' rules that would be pretty helpful.
reminder
Blogs that do not EXPLAIN something and ASK a question will not receive full credit. The point of this is not to summarize the week. READ your handout!!
Sunday, September 6, 2009
Post #3
We started last week off with reviewing what we learned from the week before last, and we also reviewed for out test Wednesday. On Thursday and Friday we learned about graphs. We learned about decreasing, increasing, concave up, concave down, positive slope, negative slope, max, min, horizontal tangent, extrema, point of inflection, and critical points.
Well that test we had I don’t think I did to well because I still iz doo doo at doing derivatives and all of that other stuff.
Well the graphs and all those words that I said up their ^^^^ that I really want to repeat because I need 250 words and im saying all this to get those words without repeating the words up their O.o well anyways Thursday and Friday was easy. I believe I grasp the graph stuff because I studied it because I fell asleep in class thrusday or Friday I don’t really remember.
So since the graphs are visual I really grasped the concept of the graps because their visual so their really easy so I think we should go over the graphs again because they are easy and they are easy because they are visual and I learn a lot easier when things or visual.
By the way alex told me type that last stuff because of my shortage of words…
ZOMG…
Well that test we had I don’t think I did to well because I still iz doo doo at doing derivatives and all of that other stuff.
Well the graphs and all those words that I said up their ^^^^ that I really want to repeat because I need 250 words and im saying all this to get those words without repeating the words up their O.o well anyways Thursday and Friday was easy. I believe I grasp the graph stuff because I studied it because I fell asleep in class thrusday or Friday I don’t really remember.
So since the graphs are visual I really grasped the concept of the graps because their visual so their really easy so I think we should go over the graphs again because they are easy and they are easy because they are visual and I learn a lot easier when things or visual.
By the way alex told me type that last stuff because of my shortage of words…
ZOMG…
week 3 post
Okay, I wasn't at school monday or tuesday, and on wednesday there was that test... so I can only really write about what happened thursday and friday. By the way, this thing is probably going to suck because i'm rushing it because I have like no time and I forgot about it and I thought we had an extra day because tomorrow is labor day.
First, we started with vocab words, such as: increasing, decreasing, positive slope, negative slope, concave up, concave down, horizontal tangent, derivative above axis, derivative below axis, zero of derivative, maximum, minimum, and point of inflection.
First derivative test
increasing decreasing, horizontal tangent, max/min
to work this problem, you need to
take a derivitive,
set = to 0
solve for x to get max, min, horizontal tangents, extrema.
Set up intervals using step 3
plug in first derivative
to find an absolute max/min plug values from step 5 into the original function
EXAMPLE
f(x)=1.2x-sinx. Find the relative extrema of f(x) on the interval (0,2pie).
the derivative is 1/2-cos(x)
set that = to zero, so you get 1/2cos(x)=0, then cosx=1/2, then x= (cos^-1)(1/2), so then you get your critical points, which are (pie/3), and (5pie/3)
Then let's say it asked you to find the relative max's and mins
you use the points, (0, pie/3) (pie/3, 5pie/3) and (5pie/3, 2pie)
after you plug in the first one, you find out it's negative, so it's decreasing
the second one is positive, so it's increasing
the third one is decreasing
so your min=(pie/3)
and your max is (5pie/3)
this is probably a dumb question, but, one thing i don't understand is the different derivative things, like 1st, or 2nd derivative or whatever. i know in the example above it only involved the first derivative, so what exactly would a second derivative be used for? and what exactly is it?
First, we started with vocab words, such as: increasing, decreasing, positive slope, negative slope, concave up, concave down, horizontal tangent, derivative above axis, derivative below axis, zero of derivative, maximum, minimum, and point of inflection.
First derivative test
increasing decreasing, horizontal tangent, max/min
to work this problem, you need to
take a derivitive,
set = to 0
solve for x to get max, min, horizontal tangents, extrema.
Set up intervals using step 3
plug in first derivative
to find an absolute max/min plug values from step 5 into the original function
EXAMPLE
f(x)=1.2x-sinx. Find the relative extrema of f(x) on the interval (0,2pie).
the derivative is 1/2-cos(x)
set that = to zero, so you get 1/2cos(x)=0, then cosx=1/2, then x= (cos^-1)(1/2), so then you get your critical points, which are (pie/3), and (5pie/3)
Then let's say it asked you to find the relative max's and mins
you use the points, (0, pie/3) (pie/3, 5pie/3) and (5pie/3, 2pie)
after you plug in the first one, you find out it's negative, so it's decreasing
the second one is positive, so it's increasing
the third one is decreasing
so your min=(pie/3)
and your max is (5pie/3)
this is probably a dumb question, but, one thing i don't understand is the different derivative things, like 1st, or 2nd derivative or whatever. i know in the example above it only involved the first derivative, so what exactly would a second derivative be used for? and what exactly is it?
Ash's 3rd post
Okay, so, the first half of the week we reviewed for the test on Wednesday. The test, might I add, was beast, I'm not going to lie. :D
But after that, Mrs. Robinson started teaching us how to take the derivative of a graph. I admit, I was pretty confused until she clarified everything on that program. But I don't understand it 100% yet. For some reason, I just couldn't grasp it.
I get which vocab words go with which derivatives:
Original: Increasing, Decreasing, Maximum, and Minimum
First: Positive slope, negative slope, and Horizontal Tangent
Second: Concave Up and Concave down
And the special cases: Derivative above axis ( positive slope and concave up), Derivative below axis (negative slope, and concave down), and Zero of derivative (horizontal tangent, and negative slope)
But for those, is that what you do? Or only if that is what is asked, do it for those/that derivative? I'm sorry this isn't making much sense, but I'm confusing myself just typing it.
I also understand what most of the vocab translates to.
Increasing: Up [obviously]
Decreasing: Down [obviously]
Concave Up: Bowl shaped to hold water
Concave Down: Umbrella shaped to keep out water
????? Horizontal Tangent: I THINK it's a straight line? I honestly don't remember
????? Derivative above and below the axis: Does this mean that the derivative starts above/below the axis? Or does it always start on the axis, but this means whether it's going up or down?
Sorry it's so confusing, my thoughts are a mess right now. Can someone explain those terms simply for me? Thank you!
But after that, Mrs. Robinson started teaching us how to take the derivative of a graph. I admit, I was pretty confused until she clarified everything on that program. But I don't understand it 100% yet. For some reason, I just couldn't grasp it.
I get which vocab words go with which derivatives:
Original: Increasing, Decreasing, Maximum, and Minimum
First: Positive slope, negative slope, and Horizontal Tangent
Second: Concave Up and Concave down
And the special cases: Derivative above axis ( positive slope and concave up), Derivative below axis (negative slope, and concave down), and Zero of derivative (horizontal tangent, and negative slope)
But for those, is that what you do? Or only if that is what is asked, do it for those/that derivative? I'm sorry this isn't making much sense, but I'm confusing myself just typing it.
I also understand what most of the vocab translates to.
Increasing: Up [obviously]
Decreasing: Down [obviously]
Concave Up: Bowl shaped to hold water
Concave Down: Umbrella shaped to keep out water
????? Horizontal Tangent: I THINK it's a straight line? I honestly don't remember
????? Derivative above and below the axis: Does this mean that the derivative starts above/below the axis? Or does it always start on the axis, but this means whether it's going up or down?
Sorry it's so confusing, my thoughts are a mess right now. Can someone explain those terms simply for me? Thank you!
post #3 !
The third week of calculus didn’t seem as bad as the second week. Probably because it was just a review for the test on the first two days and the test was on Wednesday. We had a lot of intro to Calc on the test along with the stuff we learned in the first two weeks of Calculus. Some things on the test were points of discontinuity, like removables, jumps, infinites, finites, and vertical and horizontal asymptotes. Also, there was finding derivatives, product and quotient rule, arc trig functions, derivative of sin and cos, and other things that we learned in the first week or two of Calculus.
One thing I understood very well was how to find horizontal asymptotes. To find horizontal asymptotes, you must remember three rules.
1. If the degree on top is larger than degree on bottom, it’s infinity.
2. If the degree on top is equal to the degree on bottom, divide the coefficients.
3. If the degree on top is smaller than degree on bottom, it’s 0.
So if we were given (x^3 – 2x^4 + x + 3x^2 – 4) / (x^6), then the degree on top is smaller than degree on bottom, so the limit would be equal to 0.
Now, from what I heard, the stuff everyone learned on Thursday and Friday when I was absent was pretty difficult. I heard it was something about concavity, and I’ve never heard of that before. If anyone understands it and wants to give me a brief explanation it would be greatly appreciated :)
One thing I understood very well was how to find horizontal asymptotes. To find horizontal asymptotes, you must remember three rules.
1. If the degree on top is larger than degree on bottom, it’s infinity.
2. If the degree on top is equal to the degree on bottom, divide the coefficients.
3. If the degree on top is smaller than degree on bottom, it’s 0.
So if we were given (x^3 – 2x^4 + x + 3x^2 – 4) / (x^6), then the degree on top is smaller than degree on bottom, so the limit would be equal to 0.
Now, from what I heard, the stuff everyone learned on Thursday and Friday when I was absent was pretty difficult. I heard it was something about concavity, and I’ve never heard of that before. If anyone understands it and wants to give me a brief explanation it would be greatly appreciated :)
post 3
This past week in calculus we started off just reviewing for the test which I now feel better about than before. Then after the test on Wednesday, we started to learn derivative graphs and vocabulary for the graphs. It was a relief to finally take the test on derivatives and start to learn something new. I do not know how much longer I could have taken learning what we were learning anymore.
Reviewing for the test Wednesday on Monday and Tuesday I think was a big help to me. Even though I did study the test was still not easy even with the reviewing and studying. It was just refreshed in my head and fixed the problems I had before the test. An example is getting most of the formulas down packed into my head. There were many I did not know before then.
Also, we learned about how to get the derivative of graphs. This started off a tad confusing but I soon after figured it out and realized that it was not complicated at all. Mainly all that has to be done is use the vocabulary to get the derivative of the graph. An example is if the graph is increasing then the slope is positive and if the graph is decreasing the slope is negative.
The only thing I really have a problem with is remembering which vocabulary words go with the original function, first derivative, or second derivative. If anyone has any way that helps them remember which goes with which I would appreciate if you would let me know how you do it.
Reviewing for the test Wednesday on Monday and Tuesday I think was a big help to me. Even though I did study the test was still not easy even with the reviewing and studying. It was just refreshed in my head and fixed the problems I had before the test. An example is getting most of the formulas down packed into my head. There were many I did not know before then.
Also, we learned about how to get the derivative of graphs. This started off a tad confusing but I soon after figured it out and realized that it was not complicated at all. Mainly all that has to be done is use the vocabulary to get the derivative of the graph. An example is if the graph is increasing then the slope is positive and if the graph is decreasing the slope is negative.
The only thing I really have a problem with is remembering which vocabulary words go with the original function, first derivative, or second derivative. If anyone has any way that helps them remember which goes with which I would appreciate if you would let me know how you do it.
Post Number Three
So, the third week in calculus has passed and i feel a little better though at the beginning of the week i was pretty much ready to get murdered. The first two days we reviewed derivatives and limits and everything that was going to be on the test Wednesday. Of course I was at our infamous study group sessions, though i still don't think i did well on the test at all. I knew all the formulas, i just felt i couldn't apply them to the problems. When i practiced problems studying i did not have any problems with them but i drew a blank when the test came around. I find the arc trig formulas the easiest.
Thursday and Friday we learned new things which i actually caught onto right away. I don't care how much ricky makes fun of me atleast i understand something :) First, we learned calculus graph vocabulary which is fairly simple:
Increasing-slope going up; original
Decreasing-slope going down; original
Positive Slope- first derivative (above)
Negative Slope- first derivative (below)
Concave Up- second derivative (bowl)
Concave down- 2nd derivative (umbrella)
Horizontal Tangent
Slope=0
Derivative above axis
Derivative below axis
Zero of derivative
Maximum-original
Minimum-orignial
Extrema
If the slope is postive it is increasing while if the slope is negative the graph is decreasing.
Friday we then learned the first derivative test, step by step.
1. Take a derivative
after this you must check for pts of discontinuitys
2. Set the derivative equal to zero.
3. Solve for x to find max, mins, horizontal tangents, and extrema (critical points)
4. Set up intervals using step 3.
5. Plug in first derivative (hence that this is called FIRST derivative test)
6. To find an absolute max/min plug values from #5 into original function
Check endpoints!
All of this is pretty simple to me, especially since Mrs. Robinson elaborately showed us the graphs on the first day and tediously taught us how to read the graph. Just remember, drawing a picture always helps :)
Thursday and Friday we learned new things which i actually caught onto right away. I don't care how much ricky makes fun of me atleast i understand something :) First, we learned calculus graph vocabulary which is fairly simple:
Increasing-slope going up; original
Decreasing-slope going down; original
Positive Slope- first derivative (above)
Negative Slope- first derivative (below)
Concave Up- second derivative (bowl)
Concave down- 2nd derivative (umbrella)
Horizontal Tangent
Slope=0
Derivative above axis
Derivative below axis
Zero of derivative
Maximum-original
Minimum-orignial
Extrema
If the slope is postive it is increasing while if the slope is negative the graph is decreasing.
Friday we then learned the first derivative test, step by step.
1. Take a derivative
after this you must check for pts of discontinuitys
2. Set the derivative equal to zero.
3. Solve for x to find max, mins, horizontal tangents, and extrema (critical points)
4. Set up intervals using step 3.
5. Plug in first derivative (hence that this is called FIRST derivative test)
6. To find an absolute max/min plug values from #5 into original function
Check endpoints!
All of this is pretty simple to me, especially since Mrs. Robinson elaborately showed us the graphs on the first day and tediously taught us how to read the graph. Just remember, drawing a picture always helps :)
pzost #3
This week in calculus was an interesting one at that.....After we reviewed and did the anual study group we took a test that i thought i was prepared for. Turns out i was fooled lol The test was kinda beast. I think i could have studied a little more. But to move along with the post lol Thursday i missed class and turns out that sucks. lol there is not much i know from this week besides i need help with the notes and learning the hole first, second dirivitive stuff. While Brob was going over it in class i was picking it up a little bit when she was using the graphs, but i need help with the vocabulary stuff we talked about and a little more explanation of the process because without the graph infront of me and somebody helping me I dont know where to begin....I know it has alot to do with the fact that i missed but i dont get it. I need help with the process when i just have a problem. and for future refference dont ever miss class lol it sucks
Post #3
This week in calculus appeared to be easier than the first two weeks. The beginning of the week was just review for the test. We reviewed derivatives again which I think I finally got the hang of them (most of them anyway), and we reviewed finite and infinite limits from last year and how to find points of discontinuity and if the graph is continuous or not. To find points of discontinuity you have to factor the top and the and make cancellations if possible. Whatever cancels, you set equal to zero and that is a removable at the number you get. An example is
x^2-x-12/ (x^2-6x=9) = (x-4) (x+3)/(x+3) (x+3)
The (x+3)s cancel and you are left with (x-4)/(x+3)
To find if there are any vertical asymptotes, you have to set what is left in the bottom, after you factored equal to zero.
(x+3) = 0
Therefore, there is a vertical asymptote at x= -3
And a removable at x= -3
And I think if they come out to the same number you only have to list the vertical asymptote but I’m not exactly sure so it would be great if someone could confirm that.
If there is a point of discontinuity, then the graph is not continuous.
On Thursday and Friday this week we learned something new and the first day, I was completely lost but I think I started catching on Friday. I think the most confusing part for me is the new vocabulary words and which ones go with what derivative and I get confused on how to find if the first or the second derivative is above or below the axis.
x^2-x-12/ (x^2-6x=9) = (x-4) (x+3)/(x+3) (x+3)
The (x+3)s cancel and you are left with (x-4)/(x+3)
To find if there are any vertical asymptotes, you have to set what is left in the bottom, after you factored equal to zero.
(x+3) = 0
Therefore, there is a vertical asymptote at x= -3
And a removable at x= -3
And I think if they come out to the same number you only have to list the vertical asymptote but I’m not exactly sure so it would be great if someone could confirm that.
If there is a point of discontinuity, then the graph is not continuous.
On Thursday and Friday this week we learned something new and the first day, I was completely lost but I think I started catching on Friday. I think the most confusing part for me is the new vocabulary words and which ones go with what derivative and I get confused on how to find if the first or the second derivative is above or below the axis.
Post #3
This week in Calculus we reviewed, took our first test, and started learning something new. On Wednesday we took our first test. Wow is all I have to say to that. I defintley know my derivative formulas. Anyways, Thursday and Friday we learned some vocabulary and looked at graphs. Some of the words we talked about were increasing, decreasing, concave down, concave up, positive and negative slope, maximums, minimums, horizontal tangents, point of inflection, critical points and extrema.
I generally understand what the words mean. Like if the slope is positive it is increasing and if the graph is increasing it is positive. The same goes for decreasing and negative. Concave up is like a "bowl," and concave down is like is just the opposite. Also, if it is concave up it is positive and if it is concave down it is negative. Extrema is another word for maxs and mins that we learned about in Advanced Math. Horizontal tangents can take place at the top of a max or the bottom of a min. This is where x will equal 0 for your first derivative. The point of inflection is where the concavity changes.
We also learned how to take the first and second derivative from just a graph. The first derivative you take the derivative of the equation. Then set it equal to zero and solve for x. I believe you get your maxs and mins? I know you only have to set up intervals if they ask you to take it farther, but I don't remember how you do that. Can someone help me on that? I don't know really how to put an example for this.
This is the first time I didn't have to take home my binder for Calculus. So, I'm just going on what I think I remember from Friday. I'm sure once I look over my notes I will understand more. I do remember that it made more sense Friday than Thursday. Hopefully what we learn this week will be easier than when we were learning derivatives.
:) I'm just glad we are off Monday.
I generally understand what the words mean. Like if the slope is positive it is increasing and if the graph is increasing it is positive. The same goes for decreasing and negative. Concave up is like a "bowl," and concave down is like is just the opposite. Also, if it is concave up it is positive and if it is concave down it is negative. Extrema is another word for maxs and mins that we learned about in Advanced Math. Horizontal tangents can take place at the top of a max or the bottom of a min. This is where x will equal 0 for your first derivative. The point of inflection is where the concavity changes.
We also learned how to take the first and second derivative from just a graph. The first derivative you take the derivative of the equation. Then set it equal to zero and solve for x. I believe you get your maxs and mins? I know you only have to set up intervals if they ask you to take it farther, but I don't remember how you do that. Can someone help me on that? I don't know really how to put an example for this.
This is the first time I didn't have to take home my binder for Calculus. So, I'm just going on what I think I remember from Friday. I'm sure once I look over my notes I will understand more. I do remember that it made more sense Friday than Thursday. Hopefully what we learn this week will be easier than when we were learning derivatives.
:) I'm just glad we are off Monday.
Week #3
Well for starters, this week in Calculus we took our first test. I actually did not think it was all that bad (easier than Advanced Math tests). It did not have a lot of questions, which I liked. I think I know most of the stuff we learned this week, just a little hazzy on a few things.
We did some practice on derivatives on Monday and Tuesday for the test on Wednesday. I feel like I know derivatives to the highest knowledge. So let me do an example.
(6x + 5)(7x- 4) we should know that you plug this into the product rule (uv' + vu'). u = (6x + 5); v = (7x - 4). So when you plug in you get: (6x + 5)(7) + (7x - 4)(6). Which simplifies to: (42x + 35) + (42x - 24) = 84x + 11.
I also get how to find relative max and mins by using intervals.
But I do not know the difference between orginal/first derivative/second derivative madness. I get how to do each of them, just all the different vocabulary confuses me. Can someone clarify that for me?
Ryan
We did some practice on derivatives on Monday and Tuesday for the test on Wednesday. I feel like I know derivatives to the highest knowledge. So let me do an example.
(6x + 5)(7x- 4) we should know that you plug this into the product rule (uv' + vu'). u = (6x + 5); v = (7x - 4). So when you plug in you get: (6x + 5)(7) + (7x - 4)(6). Which simplifies to: (42x + 35) + (42x - 24) = 84x + 11.
I also get how to find relative max and mins by using intervals.
But I do not know the difference between orginal/first derivative/second derivative madness. I get how to do each of them, just all the different vocabulary confuses me. Can someone clarify that for me?
Ryan
3rd Post
This week in Calculus started off with two days of reviewing. We took a test on Wednesday. I believed I was ready for the test until I saw it and then realized that I was not prepared. Thursday and Friday we learned new concepts that are seemingly simple with many things to remember. We learned many new terms of vocabulary words and other ways to define words we knew from previous years of math.
Some of the terms we learned were increasing, decreasing, concave up, concave down, and positive and negative slopes. These terms just about explain themselves. For example, if a slope is positive it is increasing; if the graph is increasing, it’s positive. Also, if a slope is negative it is decreasing; and if it’s decreasing, it is negative.
I understand the basic concepts and definitions of this but I do not understand how to work a problem with it. I understand that slope is positive when the graph is concave up, and negative when the graph is concave down. Also, when the graph is above the x-axis, your interval would be from zero to infinity and below the x-axis intervals would be from negative infinity to zero. Maximums and minimums were also discussed this week. I realized that max and mins are only new words to describe increasing or decreasing points in a graph.
Also, we learned about taking the first derivative test. I only understand the rules, and can almost follow them but I get confused with my graphs. To take the first derivative, you must take the derivative of the equation, set it equal to zero, solve for x. After you solve for x, you will have the maximum, minimum, horizontal tangents, and extrema. If the problem asks you to step farther, you then set up intervals and plug in the first derivative into the equation. Next, plug values in from the intervals into the original equation to find the ABSOLUTE maximum and minimums. The last step would be to check your endpoints.
This is really the only thing I can explain. I can’t put it into a problem, because I get confused when that happens. I could really use someone just taking it step by step with the graphs. I don’t get confused until the graphs come along…which is kind of the whole problem. So I think I’m in trouble. If anyone can help me understand the graphs it would be appreciated.
Some of the terms we learned were increasing, decreasing, concave up, concave down, and positive and negative slopes. These terms just about explain themselves. For example, if a slope is positive it is increasing; if the graph is increasing, it’s positive. Also, if a slope is negative it is decreasing; and if it’s decreasing, it is negative.
I understand the basic concepts and definitions of this but I do not understand how to work a problem with it. I understand that slope is positive when the graph is concave up, and negative when the graph is concave down. Also, when the graph is above the x-axis, your interval would be from zero to infinity and below the x-axis intervals would be from negative infinity to zero. Maximums and minimums were also discussed this week. I realized that max and mins are only new words to describe increasing or decreasing points in a graph.
Also, we learned about taking the first derivative test. I only understand the rules, and can almost follow them but I get confused with my graphs. To take the first derivative, you must take the derivative of the equation, set it equal to zero, solve for x. After you solve for x, you will have the maximum, minimum, horizontal tangents, and extrema. If the problem asks you to step farther, you then set up intervals and plug in the first derivative into the equation. Next, plug values in from the intervals into the original equation to find the ABSOLUTE maximum and minimums. The last step would be to check your endpoints.
This is really the only thing I can explain. I can’t put it into a problem, because I get confused when that happens. I could really use someone just taking it step by step with the graphs. I don’t get confused until the graphs come along…which is kind of the whole problem. So I think I’m in trouble. If anyone can help me understand the graphs it would be appreciated.
Third Post
So this week in Calculus seemed even easier than the rest. It's funny because when I was writing my last two posts I had exactly on my mind what I wanted to write because I knew what was frustrating me or what wasn't. This week--that isn't the case. So, what did we do?
We reviewed derivatives more and more. We had a test on them Wednesday so all Monday and Tuesday we made SURE we knew those things back to back. We got plenty of worksheets to make sure that we had a good grasp on them--and I do have a good grasp.
Next thing was that we needed to study other things than derivatives for the test. We had to study discontinuity. We studied removeables, jumps, and vertical and horizontal asymptotes. For removeables, it's pretty easily done to identify. All you do is factor the top and factor the bottom completely. Then if any of the factors match, you know there is a removeable there. For vertical asymptotes, anything left on the bottom is where the asymptote is. For horizontal asymptote, there are 3 rules:
1. If the degree of the top is bigger than the degree on the bottom, there is no limit
2. If the degree on the top is the same as the degree on the bottom, you divide the coefficients
3. If the degree on the top is smaller than the degree on the bottom, then the answer is 0.
So using all of this, we have this for example (after factoring the top and bottom)
(x+3)(x+4)
------------
x(x+1)(x+3)
So we know that there is a removeable at x=-3.
There are vertical asymptotes at x=0 and x=-1.
There is a horizontal asymptote at y=0 because the degree of the top is 2 which is less than 3.
Thursday we started to learn new things like concavity, the graphs of derivatives and other things...but I'm not sure if I grasps all of that completely because I wasn't there friday to go over it again. :-\
Hopefully maybe someone can go over it all with me and the applications of it. Please. :-)
-John
We reviewed derivatives more and more. We had a test on them Wednesday so all Monday and Tuesday we made SURE we knew those things back to back. We got plenty of worksheets to make sure that we had a good grasp on them--and I do have a good grasp.
Next thing was that we needed to study other things than derivatives for the test. We had to study discontinuity. We studied removeables, jumps, and vertical and horizontal asymptotes. For removeables, it's pretty easily done to identify. All you do is factor the top and factor the bottom completely. Then if any of the factors match, you know there is a removeable there. For vertical asymptotes, anything left on the bottom is where the asymptote is. For horizontal asymptote, there are 3 rules:
1. If the degree of the top is bigger than the degree on the bottom, there is no limit
2. If the degree on the top is the same as the degree on the bottom, you divide the coefficients
3. If the degree on the top is smaller than the degree on the bottom, then the answer is 0.
So using all of this, we have this for example (after factoring the top and bottom)
(x+3)(x+4)
------------
x(x+1)(x+3)
So we know that there is a removeable at x=-3.
There are vertical asymptotes at x=0 and x=-1.
There is a horizontal asymptote at y=0 because the degree of the top is 2 which is less than 3.
Thursday we started to learn new things like concavity, the graphs of derivatives and other things...but I'm not sure if I grasps all of that completely because I wasn't there friday to go over it again. :-\
Hopefully maybe someone can go over it all with me and the applications of it. Please. :-)
-John
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