Solving Limit to inf Problem: Use Indeterminate Forms & l'Hospital's Rule

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Hi, I have a limit question which I can't find out the answer to.
I think using indeterminate forms and l'hospital's rule is the solution in doing this but can't find out the right way to set it up.

[PLAIN]http://img130.imageshack.us/img130/662/lim.png

Any help would be appreciated.
 
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chocolatedady said:
Hi, I have a limit question which I can't find out the answer to.
I think using indeterminate forms and l'hospital's rule is the solution in doing this but can't find out the right way to set it up.

[PLAIN]http://img130.imageshack.us/img130/662/lim.png

Any help would be appreciated.

What if you write your function as follows?

{{(1-5/x)^{1/3}-1}\over{1/x}}
 
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Awesome, thanks a lot man! -5/3 for the answer
 

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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