Question

How do you find `lim (x^2+4)/(x^2-4)` as `x->2`?

Answer 1

There is no such limit.

Explanation:

The function has vertical asymptotes at x =-2 and x = +2. Informally, `x to oo` as `x to 2`.

Furthermore, as `x to +-oo`, the function `to` 1, because the coefficients of the highest power of `x` in the numerator polynomial is the same as that in the denominator polynomial.