$Q11.$ The root $of$ equation $cosx=x{e}^{x}istobe$ found using

Newton$-$Raphson iterations. The derivatives are given $as$

$\frac{d(cosx)}{dx}=-sinx,\frac{d(x{e}^x)}{dx}=x{e}^x+e^x$

$At$ iteration #$0,x=1(the$ initial value$).$ What $is$ the value $ofxat$

iteration #$2?Be$ accurate $to$ five decimals points.

$x_{k+1}=x_k-\frac{f(x_k)}{f^{\text{'}}(x_k)}$

$Q12.$ When you fit a linear function $to$ the given data, what

will $be$ the slope $of$ the function?

$\left[\begin{array}{cc}n& {\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i\\ {\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i& {\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i^2\end{array}\right]\{[a_0],[a_i]\}=\{[{\displaystyle \underset{i=1}{\overset{n}{}}}{y}_i],[{\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i{y}_i]\}$

$xy$

$14$

$45$

$56\mathrm{.}5$