Question

lim x-> infinity (1+e^3x)^1/5x

Could someone help me solve this question.

Thanks.

Answer 1

3/5

Answer 2

Answer is 1

Since 1/5x goes to zero when x goes to infinity and anything with the power zero is equal to 1

Answer 3

\[\lim_{x\rightarrow \infty}(1+e^{3x})^{\frac{x}{5}}\]?

Answer 4

Yes, but its 1/5x instead of x/5.

Answer 5

\[\lim_{x\rightarrow \infty}(1+e^{3x})^{\frac{1}{5x}}\]?

Answer 6

Yep :D

Answer 7

Then the answer is not 1 nor 3/5.

Evaluate the limit of the log of this expression.

Answer 8

what jamesj said. the limit of the log is 3/5

Answer 9

@jamesj i have a question maybe you would be willing to answer in chat

Answer 10

So would I just plug infinity in all of the x?

Answer 11

no the way you want to solve a limit where the variable is in the exponent is first take the log, then take the limit, then "exponentiate"

Answer 12

The answer is e^(3/5)

Answer 13

i.e. take the limit of
\[\frac{1}{5x}\ln(1+e^{3x})\]

Answer 14

yes exactly. (@sat73, don't know if you missed my comment in chat; it's there.)

Answer 15

you get
\[\frac{\infty}{\infty}\] and then you can use l'hopital

Answer 16

oh i missed it but i will look, thanks

Answer 17

Oh okay, alright thank you for your help.