Q 74. - Calculus

Question

Find the limit.

$\underset{x\to 0}{\lim }\frac{x^{2}cot x}{\sin x}$

Step-by-Step Solution

Answer

Answer is 1.

Step 1. Given information

Limit function is $\underset{x\to 0}{\lim }\frac{x^{2}cot x}{\sin x}$

Step 2. Explanation

$\begin{array}{rcl}\underset{x\to 0}{\lim }\frac{x^{2}cot x}{\sin x}& =& \underset{x\to 0}{\lim } \frac{x^2\cos x}{{\sin }^{2}x}\\ & =& \underset{x\to 0}{\lim }\frac{{\cos }^{2}x}{{\displaystyle \frac{{\sin }^{2}x}{x^2}}}\\ & =& {\cos }^{2}0\\ & =& 1\\ & & \end{array}$