Question

### Gauthmathier8739

Grade 12 · 2021-01-10

Which of the following is the Taylor series for f(x)=x^{2}\sin x about x=0? （ ）

Good Question (76)

Answer

5(808) votes

### Gauthmathier5541

Grade 12 · 2021-01-10

Answer

D

Explanation

The correct answer is (D).

\sin x=x-\dfrac {x^{3}}{3!}+\dfrac {x^{5}}{5!}-\dfrac {x^{7}}{7!}+\dots

x^{2}\sin x=x^{2}\left(x-\dfrac {x^{3}}{3!}+\dfrac {x^{5}}{5!}-\dfrac {x^{7}}{7!}+\cdots\right)=x^{3}-\dfrac {x^{5}}{3!}+\dfrac {x^{7}}{5!}-\dfrac {x^{9}}{7!}+\dots

\sin x=x-\dfrac {x^{3}}{3!}+\dfrac {x^{5}}{5!}-\dfrac {x^{7}}{7!}+\dots

x^{2}\sin x=x^{2}\left(x-\dfrac {x^{3}}{3!}+\dfrac {x^{5}}{5!}-\dfrac {x^{7}}{7!}+\cdots\right)=x^{3}-\dfrac {x^{5}}{3!}+\dfrac {x^{7}}{5!}-\dfrac {x^{9}}{7!}+\dots

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