Evaluate the following limits:

Question:

Evaluate the following limits:

$\lim _{x \rightarrow 0} \frac{\sin (x / 4)}{x}$

 

Solution:

To Find: Limits

NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form.

In this Case, indeterminate Form is $\frac{0}{0}$

Formula used: $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$

So, by using the above formula, we have

$\lim _{x \rightarrow 0} \frac{\sin (x / 4)}{x}=\lim _{x \rightarrow 0} \frac{\sin (x / 4)}{4(x / 4)}=\frac{1}{4}$

Therefore, $\lim _{x \rightarrow 0} \frac{\sin (x / 4)}{x}=\frac{1}{4}$

 

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