would someone please help me find the limit of (e^-x + 2cos(3x) as x approaches inifinity? I'm stuck on the math. I came up with 0 as an answer, but I think I'm wrong. Would someone help me break it down step by step to find my error? Thank you.

Question

would someone please help me find the limit of (e^-x + 2cos(3x) as x approaches inifinity?  I'm stuck on the math.  I came up with 0 as an answer, but I think I'm wrong.  Would someone help me break it down step by step to find my error?  Thank you.

anonymous · Answer

$$\lim_{x\to \infty} e^{-x}=0$$ but $\lim_{x\to \infty}\cos(x)$ does not exist, as cosine is periodic

anonymous · Answer

cosine oscillates between -1 and 1 infinitely often

anonymous · Answer

ok..I see what you are saying...so in this case because the two limits are not equal, then this limit does not exist...is that what you are saying?