Question

How do you find the Limit of `sqrt (x -1) / (sqrt(x+3) - 2)` as x approaches 1?

Answer 1

`oo`

Explanation:

Rationalizing the denominator

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

then

`lim_{x->1}sqrt (x -1) / (sqrt(x+3) - 2) =lim_{x->1}(sqrt(x+3)+2)/sqrt(x-1)=oo`