- #1

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## Homework Statement

[tex]\lim_{t\rightarrow \infty } t^{\frac{1}{t}}[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]let \ y = x^{\frac{1}{x}}[/tex]

[tex]\ln y = {\frac{1}{x}} ln x[/tex]

[tex]\lim_{x\rightarrow \infty } ln y = \lim_{x\rightarrow \infty } {\frac{ln x}{x}}[/tex]

L'H

[tex]\lim_{x\rightarrow \infty } ln y = \lim_{x\rightarrow \infty } {\frac{\frac{1}{x}}{1}} = \frac{0}{1} = 0[/tex]

Wolfram shows the answer to be 1 and intuition says that a^0 = 1 so i am not sure where my error is.