Question

How do you evaluate the limit `(x^2-25)/(x^2-4x-5)` as x approaches 0?

Answer 1

Factor both the numerator and the denominator to see what, if anything you can eliminate.

`=>lim_(x->0)((x + 5)(x- 5))/((x - 5)(x + 1))`

`=>lim_(x->0)(x+ 5)/(x + 1)`

`=>5/1`

`=> 5`

We could have also just substituted the given value into the expression, except it's important to learn how to do the above method when substituting isn't possible.

Hopefully this helps!