Official AP Calculus Thread for 2009

<p>Can anyone explain why on 4d from
<a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;
that you integrate from 1 to -5? and not from -5 to 1</p>

<p>Can anyone tell me if the distance traveled by a particle along a function is the same thing as the arc length for the function with respect to the bounds?</p>

<p>Thanks AxeBack.</p>

<p>By the way can someone explain how to get the answer for this question?</p>

<p>lim (2x^6+6x^3)/(4x^5+3x^3)
x->0</p>

<p>The answer is 2, but I don’t know how they got that.</p>

<p>The fuction f has derivatives of all orders of all real numbers. f^4(x) = e^(sinx). If the third-degree Taylor polynomial for f about x= 0 is used to approximate f on the interval [1,0] what’s the lagrange error bound ofor the max error on the interval [1,0].
Can anyone give me the detail answer?</p>

<p>adl, factor. :)</p>

<p>Adi, I believe in that case you factor to find the limit. You factor out 2x^3 on top, and factor out x^3 on bottom, which allows you to cancel x^3. Then, you just plug 0 back in.</p>

<p>adl0816:</p>

<p>Lol can’t believe I remember how to do this. So:
Factor out a 2x^3 from the top and factor out a x^3 from the bottom.
The (x^3) on the top cancels with the (x^3) at the bottom.
Plug in zero now, and you get two.</p>

<p>Why am I getting the vibe that this year’s Calc will be a lot harder than the previous recent years?</p>

<p>adl0816, factor out x^3 from numerator and denominator, cancel it out then plug in 0 for x and solve</p>

<p>Yeah I just figured that out too. Haha thanks though.</p>

<p>On the other hand, I have yet another problem.</p>

<p>f(x)={x^2-3x+9 for x less than or equal to 2
{kx+1 for x greater than 2</p>

<p>What value of k will make f continuous at x=2?</p>

<p>Just set them equal to each other when x = 2 so you have (2^2 -3(2) +9) = 7 = 2k +1 so K is equal to 3.</p>

<p>or lhopitals rule!</p>

<p>Does anyone know how to calculate trapezoidal riemann sums? Is it just the average of the left and right for each interval?
Does anyone also know how to calculate middle sums?</p>

<p>Wow thanks PKWsurf21! I never thought it would be this simple.</p>

<p>You know when you have to find volume when given what shape the perpendicular cross-sections are? What shapes can they be? Just squares, equilateral/isosceles triangles and circles/semicircles, right?</p>

<p>how do you find the min and max of f(x) using a f’(x) graph and 1 initial condition?</p>

<p>I have seriously decided to not even focus anymore on the MC and am just going to spend a good hour and a half on preparing for the FRQ’s that my teacher predicted will be on the exam tomorrow.</p>

<p>Virginiafan, what did your teacher predict?</p>

<p>^ Yes, I’d like to know too, lol.</p>

<p>Btw, how long has it been since there was a full-length optimization / related rates problem on there?</p>

<p>Yeah AxeBack I think so. You won’t be able to find the volume if you don’t know the area formula for that particular shape. </p>

<p>By the way, does anyone know why when they ask you to find the volume using semicircles, you have to divide the radius by 2?</p>

<p>Exact wording of question: “The region R is the base of a solid. For the solid, the cross section perpendicular to the x-axis are semicircles. Find the volume of the solid.”</p>

<p>If the two graphs are y=20/(1+x^2) and y=2, why is the radius 10/(1+x^2) and 1 instead of 20/(1+x^2) and 2?</p>

<p>^IDK if this is right, but the semicircle’s diameter will span the entire y value, right? So, the radius would be one half of the y value.</p>