Question

How do you find the limit of `sqrt(x+1)/(x-4)` as x approaches 3?

Answer 1

`lim_{xto3}sqrt(x+1)/(x-4) = -2`

Explanation:

Let's try direct substitution.

`sqrt(x+1)/(x-4) = sqrt(3+1)/(3-4) = sqrt4/(-1)= 2/(-1) = -2`

So the function is continuous at `x = 3`.

`lim_{xto3}sqrt(x+1)/(x-4) = -2`