Find the Maclaurin series of the function $$\(f(x)=x^{2} e^{2 x}\)$$ and its radius of convergence $$\(r\)$$.
A.
\(\sum_{n=0}^{\infty} \frac{2^{n+1}}{(n+1)!} x^{n} ; r=\infty\)
B.
\(\sum_{n=0}^{\infty} \frac{4^{n}}{(n+1)!} x^{n+2} ; r=1\)
C.
\(\sum_{n=0}^{\infty} \frac{2^{n}}{n!} x^{n+2} ; r=\infty\)
D.
\(\sum_{n=0}^{\infty} \frac{2^{n}}{n!} x^{n} ; r=\frac{1}{2}\)
Exam No：AP Calculus Unit 10 Questions Set 2 Year：2024 Question No：32
Answer:
C
Knowledge points:
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
Solution:
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