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

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

\frac{d y}{d x} - 2 x y = e^{x^{2}}

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

\int \frac{3 - 18 x}{64 - 9 x ^{2}} d x

\frac{d y}{d x} = \frac{b ^{2} x}{a ^{2} y}

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