# Limit of e^(-2x) * cosx as x-> ∞

Problem statement: Find the limit of e^(-2x) * cosx as x-> ∞

Attempt at solution: I tried to say that the limit of e^(-2x) as x-> ∞ is 0, and the limit of cosx doesn't exist since it oscillates between -1 and 1 therefore the overall answer is that it doesn't exist. I was wrong however and the right answer was 0. Could someone please help?

## Answers and Replies

lanedance
Homework Helper
limit of cos(x) doesn't exist but can you put bounds on its absolute value?

whats the limit of e^(-2x) times the upper bound?

D H
Staff Emeritus
Science Advisor
Try applying the squeeze theorem.