The problems states, Evaluate the limit using L'Hopital's rule:

$\displaystyle \lim_{x \to \0}(1-5x)^{\frac{1}{x}}$

Can someone walk me through how to make this into a fraction so that I can attempt the rule? Thanks!

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- Apr 6th 2013, 04:46 PMjjtjpL' Hopital's Rule for non fraction.
The problems states, Evaluate the limit using L'Hopital's rule:

$\displaystyle \lim_{x \to \0}(1-5x)^{\frac{1}{x}}$

Can someone walk me through how to make this into a fraction so that I can attempt the rule? Thanks! - Apr 6th 2013, 09:05 PMhollywoodRe: L' Hopital's Rule for non fraction.
You take the logarithm: find $\displaystyle \lim_{x\to{0}}}\ln\left((1-5x)^{\frac{1}{x}}\right)=\lim_{x\to{0}}}\frac{\ln( 1-5x)}{x}$ and if the answer is L, the answer to the original problem is $\displaystyle e^L$.

- Hollywood