Question

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

Answer 1

4

Explanation:

You can multiply both the terms of the fraction by the same factor and get:

`lim_(x->4)((x-4)(sqrt(x)+2))/((sqrt(x)-2)(sqrt(x)+2))`

`lim_(x->4)(cancel((x-4))(sqrt(x)+2))/cancel((x-4))`

`=sqrt(4)+2=2+2=4`