Limits at Infinity – Exponential Functions Worksheet

Evaluate the limit of an exponential function as x approaches negative infinity.

Evaluate the limit of the same function as x approaches positive infinity.

Apply limit-evaluation strategies to exponential expressions presented as single terms, multi-term sums, and rational quotients.

Review how exponential terms behave in both directions before assigning the problems.

Use the answer page to compare both limits for each function.

Correct answer 7(b): the exponent 3x + 5x² + 3x⁴ tends to positive infinity as x tends to positive infinity, so the exponential tends to positive infinity, not zero.

Limit evaluation at infinity — students compute lim f(x) as x→−∞ and as x→∞ for ten distinct exponential functions.

Dominant-term analysis — for sums, quotients and the polynomial or rational exponents in problems 3–10, students analyze the dominant terms in the expression or exponent to determine each limit.

Exponential function behavior — the set spans single exponential terms, sums/differences of exponentials, and rational expressions with exponential numerators and denominators.