Q. 12 - Calculus

Question

Consider the limit expression

$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sin x}{x}$

Calculate the limit.

Step-by-Step Solution

Answer

The limit  of the expression is $\frac{2}{\mathrm{\pi }}$.

Step 1. Given

The given expression is 

$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sin x}{x}$.

Step 2. Calculation

The evaluation of the equation is 

$$\begin{gathered} \underset{x\to \frac{\pi }{2}}{\lim }{\frac{\sin x}{x}}_{} \\ ={\frac{\sin {\displaystyle \frac{\mathrm{\pi }}{2}}}{\frac{\mathrm{\pi }}{2}}}_{} \\ =\frac{1}{\frac{\mathrm{\pi }}{2}} \\ =\frac{2}{\mathrm{\pi }} \end{gathered}$$