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

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

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

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

0

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

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x^{2} y^{^{''}} + 2 x y^{^{'}} = 0

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