Question:
Evaluate the following limits:
$\lim _{x \rightarrow 0} \frac{1-\cos 3 x}{x^{2}}$
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: $\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=\frac{1}{2}$
So, by using the above formula, we have
$\lim _{x \rightarrow 0} \frac{1-\cos 3 x}{x^{2}}=\lim _{x \rightarrow 0} \frac{9[1-\cos 3 x]}{(3 x)^{2}}=\frac{9}{2}$
Therefore, $\lim _{x \rightarrow 0} \frac{1-\cos 3 x}{x^{2}}=\frac{9}{2}$