The value of is approximately

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The value of

e^{0.3}

is approximately

1.349858

. (a) Compute the absolute error when

e^{0.3}

is approximated by the second-degree Maclaurin polynomial

P_{2}(x)=1+x+\dfrac{x^{2}}{2}

. (b) Compute the absolute error when

e^{0.3}

is approximated by the fourth-degree Maclaurin polynomial

P_{4}(x)=1+x+\dfrac{x^{2}}{2}+\dfrac{x^{3}}{6}+\dfrac{x^{4}}{24}

. State which polynomial gives the more accurate approximation.