Question

The value of $\underset{x\to 0}{lim}\left(\frac{1}{x^2}-\cot x\right)$

• A. $1$
• B. $0$
• C. $\infty$
• D. Does not exist

Answer 1

Answer: (C)

$\infty$

$\underset{x\to 0}{lim}\left(\frac{1}{x^2}-\cot x\right)$

$=\underset{x\to 0}{lim}\left(\frac{\tan x-x^2}{x^2\tan x}\right)$

$\frac{0}{0}form$

$=\underset{x\to 0}{lim}\left(\frac{{\sec }^{2}x-2x}{x^2{\sec }^{2}x+2x\tan x}\right)$

$=\frac{1}{0}$ as $x\to 0$

$=\infty$