Question

Use L'Hopital's rule to find the limit
lim (x)/(e^4x) as x Approaches infinity

Answer 1

Okay since they both approach infinity when we plug that in...we can use L'Hopital here

So it states that when you get an undetermined value when plugging in your limit...you can take the derivative of both the numerator and denominator ...and then plug it in again...

So take the derivative of x
and take the derivative of e^(4x)

what do you get?

Answer 2

I'm confused on the e^(4x) part

Answer 3

Alright so using the chain rule...Take the derivative of the inside and multiply it by the derivative of the outside..

e^(4x) inside (u) = 4x outside = e^u

So derivative of 4x = 4...and derivative of e^u = e^u

so

4e^(u) but now plug back in 'u = 4x]

4e^(4x)

So we have

\[\large \frac{1}{4e^{4x}}\]

Answer 4

need help any one

Answer 5

So now you plug in your limit again...when x -> infinity....it looks like the bottom STILL approaches infinity...so we have

\[\large \frac{1}{\infty}\]

What does that approach?

Answer 6

0 right?

Answer 7

You can think about it as x is very tiny compared \( e^{4 x}\) near infinity. So the limit is zero.

Answer 8

thank you! both of you