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 :(
Sunday, October 11, 2009
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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