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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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(- 5.1) (- 4.2)

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