What is the limit as x approaches 0+of (1/x)^{x^2} ?

The limit as x approaches 0+of (1/x)^{x^2} is 1

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limit as x approaches 0+of (1/x)^{x^2}

x \to 0 + lim ((\frac{1}{x})^{x^{2}})

1

Solution steps

x \to 0 + lim ((\frac{1}{x})^{x^{2}})

Apply exponent rules

= x \to 0 + lim (e^{x^{2} l n (\frac{1}{x})})

Apply the Limit Chain Rule:

1

= 1

arccsc (x)

x \to 2 lim (x^{3} - 2 x^{2} + x + 1)

\int_{- \infty}^{0} e^{r x} d x

\int 8 e^{\frac{x}{2}} d x

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{5})

What is the limit as x approaches 0+of (1/x)^{x^2} ?
The limit as x approaches 0+of (1/x)^{x^2} is 1