Find the Maclaurin series for the function. (Use the table of power series for elementary functions.) f(x)=frac{e^{x^4}}{4}

Rivka Thorpe

Rivka Thorpe

Answered question

2020-10-21

Find the Maclaurin series for the function. (Use the table of power series for elementary functions.)
f(x)=ex44

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2020-10-22Added 92 answers

The Maclaurin Series is shown below:
f(x)=f(0)+f(0)x+f(0)2!x2+f(0)3!x3+...+fn(0)n!xn+...
Here, f(x)=ex44
Finding the values:
f(0)=e04=14
f(x)=4x3ex44
f(x)=3x2ex4+4x6ex4
Similarly, f(0)=0 and f(0)=0
Thus, the Maclaurin series for the function about x=0 is,
f(x)=f(0)+f(0)x+f(0)2!x2+f(0)3!x3+...+fn(0)n!xn+...
=14+0+0+0+...+0+...
ex44=14
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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