Question

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

Answer 1

`1/4`

Explanation:

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

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