Mathematics

Problem

Let

P_{2}(x)

be the degree-2 Taylor polynomial for

f(x)=\sqrt{x}

centered at

x=4

. Which of the following is the best numerical upper bound for

|\sqrt{4.2}-P_{2}(4.2)|

? a)

9.38\times 10^{-5}

1.56\times 10^{-5}

4.17\times 10^{-5}

3.13\times 10^{-5}