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

The limit as x approaches 0 of (1/(x^2))^x is diverges

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

x \to 0 - lim ((\frac{1}{x ^{2}})^{x}) = e^{0 \cdot (- Does not exist)}

= diverges

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y = \frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

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