We use

$f(x)=1-\frac{x^2}{2}$

to approximate the function $cos(x).[$MATH$3800$W$24$A$1-10189572]$

a$.(2$ points$)$ Use MATLAB to plot $f(x)$ and $cos(x)$ over xin$[0,0\mathrm{.}5135]$ in the same plot.

b$.(2$ points$)$ Use MATLAB to estimate

max$\{|f(x)-cos(x)|$:xin$[0,0\mathrm{.}5135]\}$

by computing the maximum over $x$ in a grid of $245$ equidistant points in the given interval.

c$.(3$ points$)$ Compute in MATLAB both the forward error and backward error at $x=0\mathrm{.}2452.$ Use sprintf to format your output string so that they look like the following with at least $8$ decimal places:

Forward error is $-0\mathrm{.}00002342$

Backward error is $0\mathrm{.}00013492$