Okay so my question is..

lim as x approaches infinity of xe^(-x)
I put it in my calculator and when to table it gives me ERROR all the way across the board.. does that mean the limit is zero?

Question

Okay so my question is..

lim as x approaches infinity of xe^(-x)
I put it in my calculator and when to table it gives me ERROR all the way across the board.. does that mean the limit is zero?

anonymous · Answer

$\large xe^{-x}=\frac{x}{e^{x}} $

notice the denominator grows much faster than the numerator so your limit is zero...
idk why your calculator gives ERROR when the values should be getting closer to 0 though...

anonymous · Answer

@dpaInc  I tried (x)/(e^(x)) instead and the table still gives zero. But, that makes sense (what you said) thank you.

anonymous · Answer

what happens if a num grows much faster then the denom?

anonymous · Answer

yw... :)
maybe u just put it in your calculator incorrectly?

anonymous · Answer

if the numerator grows faster than the denominator, then there would be no limit.

anonymous · Answer

oh okay (: thank you!

anonymous · Answer

yw...