Question

`lim_(x -> 0) x sin  1/x` is equal to ______.

Options

• 0

• 1

• `1/2`

• does not exist

Answer 1

`lim_(x -> 0) x sin  1/x` is equal to 0.

Explanation:

Since `lim_(x -> 0) x = 0`

And `-1 ≤ sin 1/x ≤ 1`

By Sandwitch Theorem,

We have `lim_(x -> 0) x sin  1/x` = 0