Evaluate the following limits:


Evaluate the following limits:

$\lim _{x \rightarrow 0} \frac{\sin 5 x}{\sin 8 x}$



To Find: Limits

NOTE: First Check the form of imit. Used this method if the limit is satisfied 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 $\lim _{x \rightarrow 0} \frac{\sin 5 x}{\sin 8 x}=\lim _{x \rightarrow 0}\left(\frac{\sin 5 x}{5 x}\right) \times \frac{8 x}{\sin 8 x} \times \frac{5 x}{8 x}=\frac{5 x}{8 x}=\frac{5}{8}$

Therefore, $\lim _{x \rightarrow 0} \frac{\sin 5 x}{\sin 8 x}=\frac{5}{8}$


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