Power Euler limit

[wolly]

Hi I need to solve this euler limit.How can I solve it?Do You use subtitution?



[math]\lim_{x \to 3}(13-4x)^\frac{1}{x-3}[/math]I found Something on google but I don't know if this applied to this limit

 

[wolly]

[math]u=\frac{1}{x-3}[/math]Îs this a method to solve the limit?

 

[blamocur]

[math]u=\frac{1}{x-3}[/math]Îs this a method to solve the limit?

Try it. Even if it doesn't work you'll learn something.

 

[mario99]

Hi I need to solve this euler limit.How can I solve it?Do You use subtitution?



[math]\lim_{x \to 3}(13-4x)^\frac{1}{x-3}[/math]

Hint: [imath]\displaystyle \lim_{x\rightarrow 0}\bigg(1 - x\bigg)^{\frac{1}{x}} = \lim_{x\rightarrow \infty}\left(1 - \frac{1}{x}\right)^{x} = \frac{1}{e}[/imath]