APAP-CBC-23-1A• Non-Calculator

2023 AP Calculus BC Section I (Part A)

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ADVANCED PLACEMENT (COLLEGE BOARD)AP-CBC-23-1A• Official Candidate Question Paper

2023 AP Calculus BC Section I (Part A) • AP Calculus BC

base

[1 Marks]

Taylor Polynomials & Series

Worth 1 Marks • Challenging Level

What is the coefficient of

x^3

in the Maclaurin series for

f(x) = e^{2x} \sin(x)

Formula Guide:

Expand series:

e^{2x} = 1 + 2x + \frac{(2x)^2}{2!} + \frac{(2x)^3}{3!} + \cdots = 1 + 2x + 2x^2 + \frac{4}{3}x^3

\sin(x) = x - \frac{x^3}{6} + \cdots

. Terms yielding

x^3

1 \cdot (-\frac{x^3}{6}) + (2x^2) \cdot x = -\frac{1}{6} + 2 = \frac{11}{6}

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