Question

How do you evaluate the limit of `lim ((x+2)^2-4)/x` as `x->0`?

Answer 1

`4`

Explanation:

The function evaluated at x = 0 is `0/0` that is indeterminate.

Expand the numerator.

`(x^2+4x+4-4)/x=(x^2+4x)/x=x+4`

`lim_(xto0)((x+2)^2-4)/x=lim_(xto0)(x+4)=4`