Question

lim [(e^-x)*cos(x)] as x approaches -infinity.. Thanks!

Answer 1

so:
\[\lim_{x \rightarrow \infty}(e^{-x}\cos(x))\]

Answer 2

we know that cos(x) must be between 1 and -1, always

Answer 3

we also know that:
\[\lim_{x \rightarrow \infty}e^{-x} = 0\]

Answer 4

from that knowledge, we can say that the limit will go to 0

Answer 5

I wanted to solve for x approaches minus infinity, hence e^infinity = infinity. And cos(x) ranges between -1 and 1.. so I dont know how to determine whether it should be plus or minus.

Answer 6

Cant we do taylor expansion

Answer 7

@KubaSp remember, although x is going to infinity,\[e^{-x}\]
is going to:
\[e^{-\infty} = 0\]

Answer 8

use squeeze theorem.

Answer 9

@experimentX pretty much

Answer 10

But how to use it?

Answer 11

it must be between:
\[0\cos(1) = 0\]
and \[0\cos(-1) = 0\]

Answer 12

@MrMoose but if you have e^-(-infinity), then it should be the same as e^infinity right?

Answer 13

um... hold on, typo in my last post

Answer 14

should be cos(0) = 1, and cos(pi) = -1