Limit of e^(-2x) * cosx as x-> ∞

[TsAmE]

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?

 

[lanedance]

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]

Try applying the squeeze theorem.