Values for $f(x)=e^{-x}-1+x$ are given $in$ table.

$a{f}^{\text{'}}(1)$

$b{f}^{\text{'}}(1)$ and find error bounds for

the three$-$point midpoint formula.

Let $f(x)=x^{2}lnx+1.$ Use the second derivative formula $to$ approximate

$f^{\text{'}\text{'}}(1)$ when $h=0\mathrm{.}2.$

Approximate the following integral using the Trapezoidal, Simpson's and

Midpoint rules.

${\displaystyle \underset{-0\mathrm{.}5}{\overset{0}{}}}xln(1+x)dx$

Approximate the following integrals using Gaussian quadrature with $n=$

$2$

${\displaystyle \underset{-1}{\overset{1}{}}}\frac{2}{x^2-4}dx$ and ${\displaystyle \underset{0}{\overset{1}{}}}{x}^2{e}^{-x}dx$