These Two Taylor Series Questions are Impossible. :'(

Test Preparation AP Test Preparation
1

<p>If you could demonstrate how to solve the two questions below, that would be great.</p>

<li>If sum of the series, a_n (x-c)^n, from n=0 to infinity, is a Taylor series that converges to f(x) for every real x, then what is f’’(c)?</li>
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<p>Answer: f’’(x)=(n-1)na_n (x-c)^(n-2)=0</p>

<p>(My question: Where does that f’’(x) (2nd derivative of f(x)) come from?)</p>

<li>At what value of x does the graph of the function represented by the Taylor series, centered at x = 1, 1 - (x - 1) + (x - 1)^2 - (x - 1)^3 + … = (-1)^n (x - 1)^n intersect the graph of y = e^x?</li>
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2

<p>Will questions like those show up on the actual exam? If so, then I'm screwed. :(
Btw, those questions are from BC Practice Exam 1 by Peterson's.</p>

3

<p>those look like they are tons harder than the ones than the prep book that i am using (PR)</p>

4

<p>that first quesiotn that you asked, i have no clue. but the second one, i know how to do it, im just too lazy to actually do it. here's how it goes:
you should know the common sum for e^x = x^n / n!. then you set that equal to the sum given, so you end up solving the equation:
x^n / n! = (-1)^n (x-1)n.</p>

5

<p>also, in the first question is the answer for the problem your answer, or the answer that the book gives</p>

6

<p>ok after looking over it looks pretty simple; you just use power rule twice and thats where the f'' comes from. You take the n and subtract the exponential by 1, then when you do it again it becomes n-2 and you take n-1 to the front along with n</p>

7

<p>Wow.
I did a few of the taylor series FRQ questions and some of the ones in Barron's, and none of them were that hard.</p>

8

<p>
[quote]
also, in the first question is the answer for the problem your answer, or the answer that the book gives

[/quote]
The answer is given by the book.</p>

9

<p>yeah, the BC Calc taylor series problems will never be that hard. they usually try to see if you can write a taylor series for a given function and ask you some other questions were you find the interval of convergence or you take the derivative of the series, etc.</p>