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4 . ( a ) Consider the power series X infty n = 0 x 2 n n ! Show that the series converges

4.(a) Consider the power series
X\infty
n=0
x
2n
n!
Show that the series converges for every x in R. Include your explanation in the handwritten answers.
(b) Use Matlab to evaluate the sum of the above series. Again, include a screenshot of your command
window showing (1) your command, and (2) Matlabs answer.
(c) Use Matlab to calculate the Taylor polynomial of order 4 of the function f(x)= e
x
2
at the point
a =0. Include a screenshot of your command window showing (1) your command, and (2) Matlabs
answer.
(d) Explain how the series from Point 4a) is related to the Taylor polynomial from Point 4c). Include
your explanation in the handwritten answers

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