vertical asymptote of lim of x goes to infinity of(4+x^2)/((square root(4-x^2)?

Answer 1

For the vertical asymptotes, we don't really care about the limit as x goes to infinity; we're more interested in the values of x for which the denominator is zero. In this case, x=2 or x=-2. The function is undefined outside those two vertical asymptotes, as we would be taking the square root of a negative downstairs. As x approaches either number from the inside (meaning, approach 2 from the left or -2 from the right), y approaches infinity. The function rises without bound.

Answer 2

Asymtote go to infinity, yes.