Question

Find the limit.
limit x-->infinity (e^-2x)*cosx

Answer 1

The equation editor won't work...

Answer 2

Limit as x approaches infinity of e to the negative 2x times cosine x.

Answer 3

We have
\[ \lim _{x\to \infty} e^{-2x} \cos x\]
now we can write this as
\[ \lim _{x\to \infty} \frac{\cos x}{ e^{2x}}\]
now as x-> infinity e^{2x}--> infinity
we know that cos x has value between -1 and 1, so we have finite term over infinite
hence the limit tend to 0
\[ \lim _{x\to \infty} \frac{\cos x}{ \infty}=0\]

Answer 4

Umm, I don't think that came out the way you wanted it to... All I see are commands.

Answer 5

Oh reload the page

Answer 6

I tried to reload, no good. :(

Answer 7

Are you able to view now?

Answer 8

No, I just tried to read the commands. Taking a course in computer science helps. I just don't bother to memorize the commands for this site.

Answer 9

We can write this as
lim (x-> infinity) e^-2x (cos x)
so
lim (x-> infinity) (cos x)/e^(2x)
as x--> infinity e^2x---> infinity
we know that
cos x lies between -1 and 1
so we have a finite no. divide by infinite , hence the limit tends to zero
lim x-> inifinity (finite)/ (infinite)=0