Q. 31 - Calculus

Question

Find the limit by hand.

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

Consider the given question,

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

Step 2. Solve the given limit.

Assume $x=\frac{1}{h}$.

When $x\to \infty$, then $h\to 0$

Using the limits,

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