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2018

AP Calculus BC
Free-Response Questions

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CALCULUS BC
SECTION II, Part B
Time—15 minutes
Number of questions—1
NO CALCULATOR IS ALLOWED FOR THIS QUESTION.

1. A Maclaurin series is the Taylor series of the function f at a=0, and is represented by the following general
form:

f (x) = ∑
n=0

f (n) (0) n
f '(0)
f ''(0) 2
x = f (0) +
x+
x + ...
n!
1!
2!

(a) Compute the Maclaurin series (first four terms and general term) for the following function
x

sin(x 2 )
x2
0

g(x) = ∫

(b) What is the interval of convergence for g(x)? Justify your answer.

x8
cos(x ) − 1+
2
(c) Compute the limit lim
x→0
x16
4

STOP
END OF EXAM