What is the Limit of (E^x+1)^1/x as x Approaches Infinity?

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Homework Statement



Lim (E^x-1)^(1/x)
x->Infinito

L'Hospital?

Homework Equations



Lim (1+1/x)^x=E
x->Infinito

The Attempt at a Solution



Help!
 
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If you want to use l'Hopital you will have to take the logarithm of the limit first. Remember e^{\ln x} =x and don't forget to show us your work!
 
Last edited:
Thank you very much for your advice.

I'm still unsure how to approach this one. Apply Ln() to the entire limit?
 
Yes write the limit as \exp(\ln[(e^x-1)^{(1/x)}]).
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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