<p>^_^ good xD</p>
<p>theyellowboss, could you please explain how you were able to do the sin(x^2)+cos(x) question? I used ti-89 to obtain the answers from my previous post, but I’m not sure how to actually do it.</p>
<p>In addition, on 3b, I had a brain fail and barely missed getting the real answer for the volume. Then on part C, I used the volume from 3b (which was incorrect) and did the operations necessary for the answer. My answer for 3c would have been correct based on my calculations of 3b. Will I still get full points for 3c?</p>
<p>i actually did the 6th derivative by hand it took me literally forever</p>
<p>tito, I don’t think you had to show any work. That was just simply looking at the graph and finding the maximum value from 0 to 1/4.</p>
<p>Yeah, I tried doing that too but I think I messed up somewhere. Does anyone know how to do it the way CollegeBoard intended it to be done?</p>
<p>for finding the series ^, you would need to simply add the terms of the cosx and sin(x^2) series you found in parts a and b. When you do that, to get the first four terms you take the four lowest degree terms and combine if there are multiples (as with x^2 and x^6). </p>
<p>The best way to do the sinx and cosx is to just memorize…or you can use the basic rules. And for sin(x^2) you just replace all the xs with x^2 in the series.</p>
<p>I’m not theyellowboss but I hope that helps.</p>
<p>For the -121 one, you need to simply take the coefficient (without the 6!) of the x^6 term in the cosx + sin(x^2) series. It is the f(6)(0) value according to the format of the taylor/macclaurin series</p>
<p>Don’t overthink it! (I used to make it harder than it was at first, but I practiced a couple of these and it was pretty straightforeward after that)</p>
<p>Hey guys, it it all right to leave exact answers instead of decimal. Like for 1b?</p>
<p>If you can get an exact answer (like a fraction or with pi) that’s fine. But not if it’s just an integral.</p>
<p>I over thought that question. Anyways, could someone answer my second question from post #122?</p>
<p>Yeah, my exact answer was sin(9)/13 or something like that.</p>
<p>What did you guys get for the perimeter question?</p>
<p>1+k+e^2k+∫√(1+4e^4k) from 0 to k.</p>
<p>The k is only in the limits.
dy/dx squared is 4e^4x</p>
<p>1+k+e^2k+∫√(1+4e^4x) from 0 to k.</p>
<p>Quick question:</p>
<p>Question 3b: The region R is rotated about the x-axis to form a solid. Find the volume, V, of the solid in terms of k.</p>
<p>I simply wrote V= pi*(integral of ((-e^2x)^2)) from k to 0 and left it at that.</p>
<p>How many points did I lose for not evaluating the integral?</p>
<p>Ugh. I feel so stupid. Why didn’t I just evaluate it?</p>
<p>@println
Is your name a reference to Computer Science? I’m not 100% sure on this, but usually on area/volume questions, it’s something like:</p>
<p>+1 point for limits
+1 point for integrand (setup)
+1 point for answer
So 2/3?</p>
<p>I thought it asked to just write the integral and not solve it?</p>
<p>I did this for 6b</p>
<p>sin(x^2) = x^2-x^6/(3!)+x^10/(5!) - x^14/(7!)</p>
<p>cos(x) = 1-x^2/(2!) + x^4/(4!) -x^6/(6!)</p>
<p>cos(x)+sin(x^2) = 1+(1-1/(2!))x^2+x^4/(4!)+x^10/(5!)</p>
<p>I had a brain fart and forgot that you can combine fractions (forgetting that 2!=2)</p>
<p>Also on part c I did -6!(1/6! + 1/3!) again I had a brain fart and didn’t think of a way to simplify it.</p>
<p>Also could someone explain to me how to do part 6d. I left it blank since I never learned anything like that.</p>
<p>collegegrabber:</p>
<p>The question reads “The region R is rotated about the x-axis to form a solid. Find the volume, V, of the solid in terms of k.”</p>
<p>It seems to be telling us to solve it and find the simplified volume, not just set up the integral to do so, but I’m not entirely sure.</p>
<p>Thoughts?</p>
<p>Thesos, I solved it on the previous page.</p>
<p>And I’m pretty sure that you needed to find the volume.
:(</p>
<p>Here is my guess at the scoring guidelines:</p>
<p>1a:
+1 for speed
+1 for acceleration vector</p>
<p>1b:
- 1 for Dy/dx at t = 3 </p>
<p>1c:
+1 for x position
+1 for y position</p>
<p>1d:
+1 integral
+1 answer</p>
<h2>+2 more points somewhere </h2>
<p>2a:
+1 for value at t = 3.5</p>
<p>2b:
+1 for trapezoidal rule
+1 for approximation
+1 for meaning</p>
<p>2c:
+1 for value
+1 for explanation</p>
<p>2d:
+1 for integral of B(t)
+1 for answer
+1 for difference</p>
<h2>+1 for units</h2>
<p>3a:
+1 for 1+k+e^2k
+1 for integral of the arclength
+1 for the limits of the arclength</p>
<p>3b:
+1 integrand
+1 answer
+1 for limits of integration</p>
<p>3c:
+1 for derivative?
+1 for substituting values in</p>
<h2>+1 for answer</h2>
<p>4a:
+1 g(-3)
+1 g(x)
+1 g(-3)</p>
<p>4b:
+1 for considering 5/2
+1 for explanation</p>
<p>4c:
+1 for identifying x = 0
+1 for explanation</p>
<p>4d:
+1 average change</p>
<h2>+1 explanation</h2>
<p>5a:
+1 for approximation</p>
<p>5b:
+1 for second derivative
+1 for under approximation and why</p>
<p>5c:
+1 separation of variables
+2 antiderivatives
+1 constant of integration
+1 uses initial condition</p>
<h2>+1 solves for y</h2>
<p>6a:
+1 for sin(x)
+1 for sin(x^2)</p>
<p>6b:
+1 for cos(x)
+3 for taylor series of f(x)</p>
<p>6c:
+1 value</p>
<p>6d:
+2 showing error bound</p>