Q 75. - Calculus

Question

Find the limit.

$\underset{x\to 0}{\lim }\frac{sec x \tan x}{x}$

Step-by-Step Solution

Answer

Answer is 1

Step 1. Given information

Limit function is $\underset{x\to 0}{\lim }\frac{sec x \tan x}{x}$

Step 2. Explanation

$\begin{array}{rcl}\underset{x\to 0}{\lim }\frac{sec x \tan x}{x}& =& \underset{x\to 0}{\lim }\frac{\sin x}{x}\frac{1}{{\cos }^{2}x}\\ & =& \underset{x\to 0}{\lim }\frac{\sin x}{x}se{c}^{2}x\\ & =& 1\left(1\right)\\ & =& 1\end{array}$