Question

lim x -> infinity

(5-2x^2/3)/((3x^3/2)-4)

Answer 1

0, since the fraction is asymptotically equal to \(\frac{1}{x}\), which is 0 as \(x\to \infty\).

Answer 2

(5-2x^2/3)/((3x^3/2)-4)
{x^3(5/x^3-3/3x)}/{x^3(3/2-4/x^3)}
(5/x^3 -3/x)/(3/2-4/x^3)

Answer 3

Does it help?