Question

How do you find the limit of `(sqrt(x+8)-3)/(x-1)` as `x->1`?

Answer 1

`1/6`

Explanation:

You would multiply the terms of the fraction by the factor `sqrt(x+8)+3`:

`lim_(x->1)((sqrt(x+8)-3)* (sqrt(x+8)+3))/((x-1)*(sqrt(x+8)+3))`

`lim_(x->1)(x+8-9)/((x-1)*(sqrt(x+8)+3))`

`lim_(x->1)cancel((x-1))/(cancel((x-1))*(sqrt(x+8)+3))`

`=1/(sqrt(1+8)+3)`

`=1/6`