Find the first four nonzero terms of the Taylor series about generated by .

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

4. Find the first four nonzero terms of the Taylor series about

a=0

generated by

f(x)=\sqrt{1+x}

. (A)

1+\frac{x}{2}+\frac{x^{2}}{8}+\frac{x^{3}}{16}

(B)

1+\frac{x}{2}-\frac{x^{2}}{8}+\frac{x^{3}}{16}

(C)

1-\frac{x}{2}+\frac{x^{2}}{8}+\frac{x^{3}}{16}

(D)

1-\frac{x}{2}-\frac{x^{2}}{8}-\frac{x^{3}}{16}