Q 76. - Calculus

Question

Find the limit.

$\underset{x\to 0}{\lim }3x^{2 }co{t}^{2}x$

Step-by-Step Solution

Answer

Answer is 3.

Step 1. Given information

Limit function is $\underset{x\to 0}{\lim }3x^{2 }co{t}^{2}x$

Step 2. Explanation

$\begin{array}{rcl}\underset{x\to 0}{\lim }3x^{2 }co{t}^{2}x & =& \underset{x\to 0}{\lim }3\frac{{\cos }^{2}x}{{\displaystyle \frac{{\sin }^{2}x}{x^2}}}\\ & =& \underset{x\to 0}{\lim }3{\cos }^{2}x\\ & =& 3\end{array}$