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