Evaluate the following limits

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, $\lim _{x \rightarrow 0} \frac{\sin 4 x}{6 x}=\frac{2}{3}$

 

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