This problem of the coding assignment will be graded manually$)$

The third order Taylor polynomial centered at x $=0$ approximating f $($x$)=$ ex is

p$3($x$)=1+$ x $+$ x$2$

$2!+$ x$3$

$3!.$

Write a python script that creates the plot with the following features:

$($a$)$ Create a python script that assigns x to the $1$D array containing $100$ evenly spaced

points between $2$ and $2.$ One option is to use:

x$1=$ np$.$linspace$(-2,2,100).($formerly x $=$ np$.$linspace$(-2,2,100))$

$($b$)$ Create the $1$D array y$1=1+$ x$1+$ x$1**2/2+$ x$1**3/6$ and the $1$D array f$1=$

np$.$exp$($x$1).$ Use these $1$D arrays and matplotlib.pyplt to create a plot of p$3($x$)=$

$1+$ x $+$ x$2$

$2+$ x$3$

$6$ and f $($x$)=$ ex$.$ Make sure that your plot has a legend that labels

p$3($x$)$ and f $($x$)$ correctly, has the label $$x$$ on the x axis, $$y$$ on the y$-$axis, and

has the title $$Taylor Approximation $1($formerly $$Taylor Approximation$).$

$($c$)$ Repeat parts a and b using x$2=$ np$.$linspace$(-5,5,100),$ y$2=1+$ x$2+$ x$2**2/2$

$+$ x$2**3/6$ and f$2=$ np$.$exp$($x$2).$ Additionally use the title $$Taylor Series $2$ in

the plot.

$($d$)$ Using the print$()$ function, describe the difference in the two plots from parts b

and c in $1$ or $2$ sentences.

$3$