Higher Limits, L'Hospital's Rule

**Del** · November 4th 2007, 08:20 AM

I can't figure out how to solve this:

= ?

Please help!

**Krizalid** · November 4th 2007, 08:55 AM

You don't need to apply that Rule, just remember that

$\forall\,x\in\mathbb R,\,\lim_{n\to\infty}\left(1+\frac xn\right)^n=e^{x}.$

And,

$\lim_{x \to \infty } \left( {1 + \frac{7}<br /> {x}} \right)^{x/5} = \lim_{x \to \infty } \left[ {\left( {1 + \frac{7}<br /> {x}} \right)^x } \right]^{1/5}$

**Del** · November 4th 2007, 09:15 AM

When I solve it, I get [1 + (Infinity / Infinity)]. I don't know what I'm doing wrong.

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