Math Help - L'Hopitals

1. L'Hopitals

Find limit of (1+2x)^(1/(2lnx))
as x approaches infinity...

Could someone help me out? Thank You!

2. Originally Posted by Morgan82
Find limit of (1+2x)^(1/(2lnx))
as x approaches infinity...

Could someone help me out? Thank You!
let $y = \lim_{x \to \infty} (1+2x)^{\frac{1}{2\ln{x}}}$

$\ln{y} = \lim_{x \to \infty} \frac{\ln(1+2x)}{2\ln{x}}$

use L'Hopital ...

$\ln{y} = \lim_{x \to \infty} \frac{\frac{2}{1+2x}}{\frac{2}{x}}$

$\ln{y} = \lim_{x \to \infty} \frac{x}{1+2x} = \frac{1}{2}$

$y = e^{\frac{1}{2}} = \sqrt{e}$