(3^(3x-2)) - 5 lim ------------------ = . . . x → ∞ (3^3x) + 3

Lim (3^(3x - 2)) - 5 / (3^3x) + 3
x→∞

Lim (3^3x-2 /3^3x) - 5 /3^3x
x→∞ .. / 1 + 3/3^3x

Lim (3^3x-3x-2) - 5 / 3^3x
x→∞ .. / 1 + 3/3^x

Lim (3^-2) - 5 /3^3x
x→∞ .. /1 + 3/3^x

= (1/9 - 5/∞) / (1 + 3/∞)

= 1/9 - 0 / 1 + 0

= 1/9 / 1

= 1/9