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

The limit as x approaches infinity of (1/x)^{1/x+1} is 0

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

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

0

Solution steps

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

Simplify

(\frac{1}{x})^{\frac{1}{x} + 1} : (\frac{1}{x})^{\frac{1}{x}} \frac{1}{x}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

x \to \infty lim (\frac{1}{x}) = 0

= 1 \cdot 0

Simplify

= 0

\int_{2}^{e^{3}} \frac{1}{x} d x

y = \frac{2 cos ( x )}{x + 1}

\int \frac{x ^{3}}{( x ^{2} + 1 )} d x

e^{- 3 x^{2}}

\frac{- s}{7 s ^{2} + 26 s + 25}

What is the limit as x approaches infinity of (1/x)^{1/x+1} ?
The limit as x approaches infinity of (1/x)^{1/x+1} is 0