Question

$\underset{x\to 0}{lim}{\sin }^{-1}\left(\right(\sec x\left)\right)$ is equal to:

• A. $\frac{\pi }{2}$
• B. $1$
• C. $0$
• D. None of the above

Answer 1

Answer: (A)

$\frac{\pi }{2}$

As $x\to 0,$ then $\sec x\to 1$

$\Rightarrow \underset{x\to 0}{lim}{\sin }^{-1}\left(\sec x\right)={\sin }^{-1}\left(1\right)=\frac{\pi }{2}$