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4 . ( a ) Consider the power series X infty n = 0 x 2 n n ! Show that the series converges
a Consider the power series
Xinfty
n
x
n
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 your command, and Matlabs answer.
c Use Matlab to calculate the Taylor polynomial of order of the function fx e
x
at the point
a Include a screenshot of your command window showing your command, and Matlabs
answer.
d Explain how the series from Point a is related to the Taylor polynomial from Point c Include
your explanation in the handwritten answers
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