Q. 32 - Calculus

Question

Find the limit by hand.

$\underset{x\to 0}{\lim } x \sin \frac{1}{x}$

Step-by-Step Solution

Answer

On solving the limit, we get, $0$.

Step 1. Given information.

Consider the given question,

$\underset{x\to 0}{\lim } x \sin \frac{1}{x}$

Step 2. Solve the given limit.

Using the product rule,

$$\begin{gathered} =\underset{x\to 0}{\lim } x \underset{x\to 0}{\lim } \sin \frac{1}{x} \\ =0 \sin \frac{1}{0} \\ =0 \end{gathered}$$