Question

The value of $\underset{x\to -1^{+}}{lim}{\cot }^{-1}x$ is

• A. limit does not exist
• B. $\frac{3\pi }{4}$
• C. $-\frac{\pi }{4}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B $\frac{3\pi }{4}$

Given: $\underset{x\to -1^{+}}{lim}{\cot }^{-1}x$
$=\underset{h\to 0}{lim}{\cot }^{-1}(-1+h)$
$={\cot }^{-1}(-1)$
$=\pi -{\cot }^{-1}\left(1\right)$
$(\because {\cot }^{-1}(-x)=\pi -{\cot }^{-1}(x),x\in R)$
$=\pi -\frac{\pi }{4}=\frac{3\pi }{4}$