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

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Answer 1 · 2016-04-15T00:30:07

#0#

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#