Numerical Analysis

[Guest]

This is my daughter's math problem. Sorry I can't figure out in this site how to type an exponent or less than or equal to.

Find the degree 2 Taylor polynomial for f (x) = ex(exponent) sin (x), about the point a = 0. Bound the error in this approximation when

–pi/4 < x < pi/4.

 

[pka]

\(\displaystyle y(x) = e^x \sin (x)\quad \Rightarrow \quad y(0) = 0\)
\(\displaystyle y'(x) = e^x \sin (x) + e^x \cos (x)\quad \Rightarrow \quad y'(0) = 1\)
\(\displaystyle y''(x) = 2e^x \cos (x)\quad \Rightarrow \quad y''(0) = 2\)
\(\displaystyle \sum\limits_{k = 0}^2 {\frac{{y^{(k)} (0)}}{{k!}}(x - 0)^k }\).