Evaluate Limits of a Function

Question

Find the limits lim(x)→∞ and lim(x)→−∞ e³x+1÷8−4e^3x algebraically.

Answer 1

lim(x)→∞ (e^3x + 1)/(8 - 4e^3x) = lim(x)→∞ (1 + 1/e^3x)/(8/e^3x - 4) = (1 + 0)/(0 - 4) = - 1/4.

lim(x)→ - ∞ (e^3x+ 1)/(8 - 4e^3x) = (0 + 1)(8 - 0) = 1/8