Question

How do you find the limit of `(sin(x))/(5x)` as x approaches 0?

Answer 1

The limit is `1/5`.

Explanation:

Given `lim_(xto0) sinx/(5x)`

We know that `color(blue)(lim_(xto0) sinx/(x) = 1`

So we can rewrite our given as:
`lim_(xto0) [sinx/(x)*1/5]`

`1/5 * lim_(xto0) [sinx/(x)]`

`1/5 * 1`

`1/5`