Q. 52 - Calculus

Question

Use tables of values to make educated guesses for each of the limits in Exercises 39–52. 

$\underset{x\to \infty }{\lim }\sin \left(\frac{1}{x}\right)$

Step-by-Step Solution

Answer

The value of $\underset{x\to \infty }{\lim }\sin \left(\frac{1}{x}\right)=0.$

Step 1. Given Information.

The given function is $\underset{x\to \infty }{\lim }\sin \left(\frac{1}{x}\right)$.

Step 2. Value of the limit.

Consider the table,

$x$	$10$	$100$	$1000$
$\sin \left(\frac{1}{x}\right)$	$0.0841$	$0.0084$	$0.00084$

The value of $\sin \left(\frac{1}{x}\right)$ approaches to zero as $x\to \infty .$

Therefore,

$\underset{x\to \infty }{\lim }\sin \left(\frac{1}{x}\right)=0$