Limits

[Kallistes]

Hi everyone!
I'm taking calculus in college right now and I don't know how to solve one of the problems. It's really frustrating.

The question is:
Find the limit as x approaches 1+ of x^(2/(1-x)).

I know the answer is 1/e^2, I just don't know how to get there. Could someone please help me?

 

[Deleted member 4993]

Hi everyone!
I'm taking calculus in college right now and I don't know how to solve one of the problems. It's really frustrating.

The question is:
Find the limit as x approaches 1+ of x^(2/(1-x)).

I know the answer is 1/e^2, I just don't know how to get there. Could someone please help me?

Substitute

y = 1- x

then your problem becomes:

\(\displaystyle \displaystyle \lim_{y\to 0}\left [1 - y \right ]^{\frac{2}{y}}\)

Does that limit (expression) look similar to some standard limit ?

 

[HallsofIvy]

If you do not recognise that, it might help to see that if \(\displaystyle z= (1- y)^{2/y}\) then \(\displaystyle ln(z)= (2/y)ln(1- y)\).