Question

Limit of x*e^(-x) when going towards infinity?

Answer 1

Do you know the l'hopital rule?

Answer 2

I know that rule, it's when f(x) either equals 0/0 of infinity/infinity so take the derivative of f(x)/g(x) so f'(x)/g'(x) right?

Answer 3

yep

Answer 4

try expressing that in a fraction :)

Answer 5

As a fraction it would be \[\frac{ x }{ e^x }\]Am I right?

Answer 6

yep :)

Answer 7

now you can use that rule :)

Answer 8

The derivative of e^x is still e^x?

Answer 9

yep :)

Answer 10

I know from class that it should be 0 but I'm not sure how to get that

Answer 11

What's the derivative of \(x\)?

Answer 12

It should be 1

Answer 13

So now what's the fraction?

Answer 14

\[\frac{ 1 }{ e^x }\]

Answer 15

And what does this approach when x tends to infinity?

Answer 16

Towards 0

Answer 17

exactly :)

Answer 18

Oh, I get it now, thanks for the help :)

Answer 19

no problem :)