Lim = (3(1/3)^2 + 5(1/3) - 2) / (3(1/3) - 1)

Lim = (3(1/9) + 5/3 - 2) / (1 - 1)

Lim = (1/3 + 5/3 - 2) / 0

Lim = (6/3 - 2) / 0

Lim = (2 - 2) / 0

Lim = 0 / 0

Therefore, the limit does not exist in this case because it results in an indeterminate form of 0/0.