Consider the function f$($x$)=$x$^(2)$e$^(3$x$).$ Write the first three non$-$zero terms of the

following series, and find a series formula:

a$.$ the Maclaurin series of f$($x$).$

b$.$ the Taylor series of f$($x$)$ centered at a$=1.$

Consider the function h$($x$)=5$xcos$($x$^(3)).$ Write the first three non$-$zero terms of the

following series, and find a series formula:

a$.$ the Maclaurin series of f$($x$).$

b$.$ the Taylor series of f$($x$)$ centered at a$=-(\backslash$pi $)/(2).$

Consider the function g$($x$)=$cos$(3$x$).$

a$.$ Write the first three non$-$zero terms of the Maclaurin series, and find a series

formula.

b$.$ Evaluate the limit $\backslash$lim$\_($x$->0)(1-$cos$(3$x$))/(5$x$^(2))$ by using the Maclaurin series.

Consider the function k$($x$)=$sin$($x$).$ Find the Taylor series formula when centered

at a$=(\backslash$pi $)/(3).$

For problems $1-4,$ use desmos $($or other graphing softwar$($e$)/($c$)$alculator$)$ to plot the original

given function and any series that are in the problems. EXTRA CREDIT $(2$ points for each problem$)$

For problems $1-4,$ use desmos $($or other graphing software$/$calculator$)$ to plot the original given function and any series that are in the problems.