Question

What is the limit of `(4x^2+1)/(x^2+2x-3)` as x approaches -2?

Answer 1

`-17/3`

Explanation:

`f(x) = (4x^2+1)/(x^2+2x-3)`

Like polynomials, rational functions are continuous everywhere on their domains.

In our example, the denominator is non-zero at `x=-2`, so `f(x)` is continuous in an open interval around `x=-2` and we have:

`lim_(x->-2) f(x) = f(-2) = (16+1)/(4-4-3) = 17/(-3) = -17/3`