lim x-> infinity (e^(-x)cosx) ?
First of all does the limit as x-> inifinity of cosx even exist?
I thought it would = inifinity but then again i feel like it DNE as well.
Ive atempted this problem in 2 ways, but i first would like to see if cosx as x approaches infinity even exists
The trick here is to recall that . This is important because as , is going to remain finite (but we don't necessarily know the limit value).
So the only term that will really effect the limit will be the term. So we should see that .
Does this make sense?
EDIT: skeeter beat me to it.
Ohh because i was simply trying to figure out if we use L'hospitals rule? or you can even rewrite is as cosx/e^x but i was always stuck with the cosx and then e^x would approach infinity in that case.
So you mierly just "ignored" the cos and did the limit to e^-x which is 0?