Provide an appropriate response.
-Obtain the first nonzero term of the Maclaurin series for $\sin x - \tan ^ { - 1 } x$.
A) $\frac { x ^ { 3 } } { 3 }$
B) $\frac { x ^ { 3 } } { 6 }$
C) $\frac { x ^ { 3 } } { 2 }$
D) $- \frac { x ^ { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The Maclaurin series for $\sin x$ is $x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots$. The Maclaurin series for $\tan^{-1} x$ is $x - \frac{x^3}{3} + \frac{x^5}{5} - \cdots$. Therefore, the first nonzero term of the Maclaurin series for $\sin x - \tan^{-1} x$ is $\frac{x^3}{6}$.

Provide an Appropriate Response sin⁡x−tan⁡−1x\sin x - \tan ^ { - 1 } xsinx−tan−1x

Provide an Appropriate Response $\sin x - \tan ^ { - 1 } x$