Question

How do we find the limit here? :

Answer 1

`4`

Explanation:

Rationalize the denominator by multiplying and dividing by `sqrt(x)+2`

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

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

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

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

This gives `4`