Consider the function

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

Problem

g(x)=\sqrt{1+x^{2}}

. A Taylor polynomial is to be constructed about the point

x=1

. (a) Compute

g(1)

g^{\prime}(1)

, and

g^{\prime\prime}(1)

. Provide exact values, not decimal approximations. (b) Write the second–degree Taylor polynomial

T_2(x)

for

g(x)

centered at

x=1

. (c) Use

T_2(x)

to approximate

g(1.2)

. Give the result to five decimal places.