Question:
Evaluate the following limits
$\lim _{x \rightarrow 0} \frac{\sin 4 x}{6 x}$
Solution:
To Find: Limits
NOTE: First Check the form of imit. Used this method if the limit is satisfied any one from 7 indeterminate forms.
In this Case, indeterminate Form is $\frac{0}{0}$
Formula used: $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$
So $\lim _{x \rightarrow 0} \frac{\sin 4 x}{6 x}=\lim _{x \rightarrow 0}\left(\frac{\sin 4 x}{4 x}\right) \times \frac{4}{6}=\frac{4}{6}=\frac{2}{3}$
Therefore, $\lim _{x \rightarrow 0} \frac{\sin 4 x}{6 x}=\frac{2}{3}$