# Evaluate the limit. \lim_{x \rightarrow \pi/2} \sin(x/2)-\cos(x/3)

## Question:

Evaluate the limit.

{eq}\displaystyle \lim_{x \rightarrow \pi/2} \sin(x/2)-\cos(x/3) {/eq}

## Limits:

We have a function which has sine and cosine terms. There are many methods to evaluate the limits like L hospital's rule, factorization, etc. Here we will directly apply the limits.

$$\lim_{x \rightarrow \pi/2} \sin(x/2)-\cos(x/3) \\$$

We will directly apply the limits:

$$\sin(\pi/4)-\cos(\pi/6)\\ \frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\\ \frac{\sqrt{2}-\sqrt{3}}{2}$$

Understanding the Properties of Limits

from Math 104: Calculus

Chapter 6 / Lesson 5
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