Question

PLEASE HELP
L’Hopital’s Rule

Answer 1

1/4

Explanation:

Find the following limit:

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

((3 x + 2)^(1/3) - 2)/(x - 2) = (((3 x + 2)^(1/3) - 2) (4 + 2 (3 x + 2)^(1/3) + (3 x + 2)^(2/3)))/((x - 2) (4 + 2 (3 x + 2)^(1/3) + (3 x + 2)^(2/3))) = 3/(4 + 2 (3 x + 2)^(1/3) + (3 x + 2)^(2/3)):

lim_(x->2)(3/(4 + 2 (3 x + 2)^(1/3) + (3 x + 2)^(2/3)))

lim_(x->2) 3/(4 + 2 (3 x + 2)^(1/3) + (3 x + 2)^(2/3)) = 3/(4 + 2 (3 2 + 2)^(1/3) + (3 2 + 2)^(2/3)) = 1/4:

Answer: 1/4