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Homework Statement
\lim_{t\rightarrow \infty } t^{\frac{1}{t}}
Homework Equations
The Attempt at a Solution
let \ y = x^{\frac{1}{x}}
\ln y = {\frac{1}{x}} ln x
\lim_{x\rightarrow \infty } ln y = \lim_{x\rightarrow \infty } {\frac{ln x}{x}}
L'H
\lim_{x\rightarrow \infty } ln y = \lim_{x\rightarrow \infty } {\frac{\frac{1}{x}}{1}} = \frac{0}{1} = 0
Wolfram shows the answer to be 1 and intuition says that a^0 = 1 so i am not sure where my error is.