Evaluate the following limits:
Question:

Evaluate the following limits:

$\lim _{x \rightarrow 0} \frac{\sin x \cos x}{3 x}$

 

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

$\lim _{x \rightarrow 0} \frac{\sin x \cos x}{3 x}=\lim _{x \rightarrow 0} \frac{\sin x}{x} \times \frac{\cos x}{3}=\frac{1}{3}$

Therefore, $\lim _{x \rightarrow 0} \frac{\sin x \cos x}{3 x}=\frac{1}{3}$

 

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