Q. 23 - Calculus

Question

Find the limit by hand.

$\underset{x\to 0}{\lim }\frac{3x}{\sin 2x}$

Step-by-Step Solution

Answer

On solving the limit, we get, $\infty$.

Step 1. Given information.

Consider the given question,

$\underset{x\to 0}{\lim }\frac{3x}{\sin 2x}$

Step 2. Solve the given limit.

Using the quotient rule,

$$\begin{gathered} =\frac{\underset{x\to 0}{\lim }3x}{\underset{x\to 0}{\lim }\sin 2x} \\ =\frac{3\left(0\right)}{\sin \left(2·0\right)} \\ =\frac{0}{\sin 0} \\ =\frac{0}{0} \\ =\infty \end{gathered}$$