Limit of exponential function at infinity

In this video, I showed how to find the limit of an exponential log function

[carolnoelle]

Great explanations and smooth chalk. Thanks!

[ebrimagajaga]

Yeah thank you so I have learned from your Additionally the question can be solved by easily plugging large positive numbers e.g 100, 10000, etc, each of these would directly give answer as exactly 1. Thank you! I love the way you've delivered the lesson

[utuberaj]

Great derivation using LH rule- but with the ln idea

[WagesOfDestruction]

nice, I solved it by inspection by saying e^-x when x-> inf is 0. so inf^0 ->1. => answer =1

[rangaweerakkody]

I would do it as a two part problem. First I will show that y = e^-x when lim->inf y ->0. Then x^y when y->0 would be x->1.

[Ennio]

Let e^(-x)=y then y goes to zero
So lim when x goes to infinity of x^[e^(-x)] = lim when y goes to ZERO of (- ln(y))^y
Since lim (-ln(y)) at 0 =+ infinity
lim y at 0 =0
Then lim at 0 of (-ln y)^y = 1
It's a limit of a power with a base coming greater but the exponent is going to zero .
Thank you for your efforts, but I hope you'll be convicted 😂I usually avoid L'HOSPITAL'S

[suyunbek]

now do the derivative of p to the eye to the am to the p
i like good kitty as i like good tea

[salahbekhit]

The limit of the natural logarithm is not always equal to the natural log of the limit
The conditions for equality are continuity, and boundedness
We should mention at least the continuity in our problem
Good work, but not perfect