Question

How do you find the limit of `(x^2 - 25) / (x^3 - 125)` as x approaches 5?

Answer 1

Factor and reduce.

Explanation:

Since `5` is a zero of both the polynomials, we know that `x-5` is a factor of both.

`x^2-25 = (x-5)(x+5)`

`x^3-125 = (x-5)(x^2+5x+25)`

`lim_(xrarr5)(x^2-25)/(x^3-125) = lim_(xrarr5)((x-5)(x+5))/((x-5)(x^2+5x+25))`

`= 10/75 = 2/25`