Use zeroth$-$ through fourth$-$order Taylor series expansions to predict f$(5)$ for

$()=25463+7288$

Use a base point at x $=1,$ and compute the true percentage error for each

approximation. $($Round the final estimated values to the nearest whole numbers and the

error values to two decimal places.$)$ Enter the desired values in the spaces provided in

Canvas.

Problem $7(20$ points$)$

Write a MATLAB program or Excel macro that will solve for sin$($x$)$ using the infinite

series below. The program should have $2$ inputs: the value of x and the stopping

criterion $($i$.$e$.$ maximum desired true fractional error$).$ Loop and add terms until the true

fractional error is less than the stopping criterion. Report the approximate value of sin$($x$)$

and the number of terms needed.

$()=3$

$3!+5$

$5!...==0$

$\backslash$infty

$(1)(2+1)$

$(2+1)!$

Order Value Error $\backslash$epsi $||\%$

$0??$

$1??$

$2?84\mathrm{.}98$

$3??$

$414610?$