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Determine the power series of f(x) = xe^x about the value a = 0. To receive full credit you must explain how you obtained the series and write this series using both summation notation sum cnxn from n...

Determine the power series of f(x) = xe^x about the value a = 0. To receive full credit you must explain how you obtained the series and write this series using both summation notation

sum cnxn from n=0 to infinity  and as an “infinite” polynomial f (x) = c0 + c1 x + c2 x2 + · · · .

(a) Use the first SIX terms of the series from part (a) to obtain a decimal approximation for the number e.

(b) Use the first THREE terms of the series from part (a) to obtain an approximation of integral (xe^x) dx from 0 to 1

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