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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

y^{^{''}} + 16 y = cos (4 x) + sin (4 x)

\int + \frac{x ^{2}}{1 - 2 x ^{3}} d x

n = 0 \sum \infty \frac{( n - 1 )}{n}

\int_{1}^{3} (x^{2} - 4 x + 3) d x

\frac{d}{d x} (2 x^{2} - 7 x)

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