# Higher Limits, L'Hospital's Rule

• November 4th 2007, 08:20 AM
Del
Higher Limits, L'Hospital's Rule
I can't figure out how to solve this:

https://webwork.math.lsu.edu/webwork...aa0c13e961.png = ?

• November 4th 2007, 08:55 AM
Krizalid
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,

$\lim_{x \to \infty } \left( {1 + \frac{7}
{x}} \right)^{x/5} = \lim_{x \to \infty } \left[ {\left( {1 + \frac{7}
{x}} \right)^x } \right]^{1/5}$
• November 4th 2007, 09:15 AM
Del
When I solve it, I get [1 + (Infinity / Infinity)]. I don't know what I'm doing wrong.