Question

lim as x --> infinity
( 4x + (3 / x^2) )

My work:
(4x^3 / x^2) + (3 / x^2)

(4x^3 + 3) / x^2

degree of top > degree of bottom

No horizontal asymptote, so the limit does not exist

The correct answer is infinity. How?

Answer 1

Also:

lim x → 0 (-x^2 + 4) / (x^2 - 1)

I got -1, but the right answer is -4

Answer 2

#1 is correct, but could be done directly. 3/x^2 -> 0

so, the limit is just 4x, which -> ∞

For #2, no tricks are involved. x^2 -> 0, so

-(x^2-4)/(x^2-1) -> -(0-4)/(0-1) = -4