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.

Assign problems in order, since structural complexity increases from a single exponential term (problem 1) to multi-term sums (problem 3) and quotients of several exponential terms (problems 5, 6 and 9).

Have students check both limit answers per problem against the second page, which lists the x→−∞ and x→∞ results side by side for all ten problems.

Review dominant-term reasoning before assigning the set, since several problems — problem 6's quotient of six exponential terms, for example — require identifying which exponential term grows fastest as x moves toward each infinity.

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

Dominant-term analysis — for the multi-term sums and quotients in problems 3-10, students identify which exponential term grows fastest to determine each limit.

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