Using l'hopital's rule:

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

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

(5sin(2x) ÷ (3x))
(10cos(2x) ÷ (3))
(10cos(0) ÷ (3))
The limit is 10/3

(6x² - 4x + 2) / (2x³ + 2x² -5x -4)
(12x - 4) / (6x² + 4x - 5)
(12) / (12x + 4)
The limit is 0

1) 10cos(2x)/3 = 10/3