Consider the function .

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the function

p(x)=e^{x^{2}}

. (1) Derive the first four non-zero terms of the Maclaurin series for

p(x)

and write them in ascending powers of

x

. (Express the series through the power of

x^{6}

.) (2) Use the third–degree Maclaurin polynomial you found in part (a) to approximate

p(0.2)=e^{0.04}

. Record your answer to six decimal places. (3) The calculator value of

e^{0.04}

1.04081077

. Compute the absolute error of your approximation from part (b) and state the error to eight decimal places.