Question

What is the limit as `x -> ∞` of `e^(-2x)cosx`?

Answer 1

`0`

Explanation:

Remember that

`-1<=cosx<=1=>-e^(-2x)<=e^(-2x)*cosx<=e^(-2x)`

Hence

`lim_(x->oo)-e^(-2x)<=lim_(x->oo)e^(-2x)cosx<=lim_(x->oo)e^(-2x)`

But `lim_(x->oo)-e^(-2x)=lim_(x->oo)e^(-2x)=0`

Hence

`lim_(x->oo)e^(-2x)cosx=0`