Question

How do you evaluate the limit `sinx/(5x)` as x approaches `0`?

Answer 1

The limit is `1/5`

Explanation:

`lim_(x->0)sinx/(5x)=0/0`

This is not possible, so we us l'Hôpital's rule.

`lim_(x->0)sinx/(5x)=lim_(x->0)((sinx)')/((5x)')`

`lim_(x->0)cosx/(5)=cos0/5=1/5`

graph{sinx/(5x) [-1.884, 1.96, -0.53, 1.392]}