Use L'Hopital's Rule

1. lim as x goes to 0: 5 sin 2x/3x

2. lim as x goes to infinity: 6x^2 - 4x +2/2x^3 + 2x^2 - 5x -4

1. lim x -> 0:
5 sin 2x/3x
differensiate both nominator and denominator

Lim x-> 0
5*2 cos2x / 3
= 5*2^1 / 3
= 10/3


2. lim x -> infinity:
6x^2 - 4x +2/2x^3 + 2x^2 - 5x -4

Lim x-> infinity
12x-4 / 6x^2 +4x -5

Lim x-> infinity
12 / 12x + 4

= 12 / infinity

= 0

.

..