Question

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

Answer 1

`- sqrt(2)`

Explanation:

We have: `lim_(x -> 3) (sqrt(x - 1)) / (x - 4)`

This limit can be evaluated by substituting `x` with `3`:

`= (sqrt((3) - 1)) / ((3) - 4)`

`= (sqrt(2)) / (- 1)`

`= - sqrt(2)`