Limits at infinity - exponential functions

Understand the concept of limits at infinity and horizontal asymptotes for exponential functions

This deck explicitly builds on a prior lesson on limits at infinity of polynomials (slide 2); review that factoring-the-dominant-term technique before this lesson so students recognize it being reapplied to exponential expressions.

Walk through the sign of the exponent's own limit first (slides 5-6) before moving to the multi-term factoring examples (slides 9-12), since later problems depend on correctly reading whether the exponent itself goes to positive or negative infinity.

Evaluating basic exponential limits at infinity — recognizing that e^x -> infinity as x -> infinity and e^x -> 0 as x -> -infinity

Applying the limit-of-a-product property when the exponent of an exponential term is itself a polynomial limit

Factoring out the dominant exponential term in a multi-term expression to evaluate a limit at infinity

Evaluating limits of rational expressions with exponential terms in both the numerator and denominator