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Write the Maclaurin series for f(x) = x^7e^x5. (2 points) a) the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial b) the summation from n equals 0 to infinity of the quotient of x to the 12th power and the quantity n plus 5 factorial c) the summation from n equals 0 to infinity of the quotient of x to the quantity 5 times n plus 7 power and n factorial d) the product of x raised to the 5 times n power and the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial

Answer :

LammettHash

Recall that

[tex]e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]

Then

[tex]e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n}}{n!}[/tex]

and

[tex]x^7e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n+7}}{n!}[/tex]

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