Evaluate the following limits:
Question:

Evaluate the following limits:

$\lim _{x \rightarrow 0} \frac{\tan (x / 2)}{3 x}$

 

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: $\lim _{x \rightarrow 0} \frac{\operatorname{tanx}}{x}=1$

So, by using the above formula, we have

$\lim _{x \rightarrow 0} \frac{\tan (x / 2)}{3 x}=\lim _{x \rightarrow 0} \frac{\tan (x / 2)}{6(x / 2)}=\frac{1}{6}$ [Divide and multiply with 2 on denominator]

Therefore, $\lim _{x \rightarrow 0} \frac{\tan (x / 2)}{3 x}=\frac{1}{6}$

 

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