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

1 Answer
Jan 21, 2018

" limit" = 0

Explanation:

lim_(x->-oo) = (x^2+2)/(x^3+x^2-1)

lim_(x->-oo) = (1/x + 2/x^3)/(1 + 1/x-1/x^3)

Putting x = -oo

(1/(-oo) + 2/(-oo)^3 )/( 1 + 1/-oo - 1/(oo)^3 ) = 0/1 =0

Therefore the expression approaches zero at negative infinity. graph{(x^2+2)/(x^3+x^2-1) [-10.25, 9.75, -5, 5]}