- #1
freezer
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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.