Also:
lim x → 0 (-x^2 + 4) / (x^2 - 1)
I got -1, but the right answer is -4
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?
2 answers
#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
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