What is the limit as x approaches infinity of (1/x)^{2/x} ?

The limit as x approaches infinity of (1/x)^{2/x} is 1

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limit as x approaches infinity of (1/x)^{2/x}

x \to \infty lim ((\frac{1}{x})^{\frac{2}{x}})

1

Solution steps

x \to \infty lim ((\frac{1}{x})^{\frac{2}{x}})

Apply exponent rules

= x \to \infty lim (e^{\frac{2}{x} l n (\frac{1}{x})})

Apply the Limit Chain Rule:

1

= 1

y^{^{''}} + 5 t y^{^{'}} - 5 y = 0

\frac{d}{d x} (ln (cosh (x)))

\frac{\partial}{\partial y} (x cos (y) + y e^{x})

\frac{d}{d x} (\frac{x ^{2} - 1}{2 x})

x \to - 2 lim (\frac{2 - x ^{2}}{4 x})

What is the limit as x approaches infinity of (1/x)^{2/x} ?
The limit as x approaches infinity of (1/x)^{2/x} is 1