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AP Calculus BC
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SECTION II, Part B
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
f (x) = ∑
f (n) (0) n
f ''(0) 2
x = f (0) +
x + ...
(a) Compute the Maclaurin series (first four terms and general term) for the following function
sin(x 2 )
g(x) = ∫
(b) What is the interval of convergence for g(x)? Justify your answer.
cos(x ) − 1+
(c) Compute the limit lim
END OF EXAM
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