What is the limit as x approaches 0+of \sqrt[x]{x} ?

The limit as x approaches 0+of \sqrt[x]{x} is 0

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limit as x approaches 0+of \sqrt[x]{x}

x \to 0 + lim (x x)

0

Solution steps

x \to 0 + lim (x x)

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

x \to 8 lim (\frac{x ^{2}}{x - 8})

x \to 3 lim (5 f (x))

x \to 0 lim (- 5)

x \to 5 lim (\frac{2 x ^{2} - 11 x + 5}{x - 5})

x \to 0 lim (\frac{4 + x}{x})

What is the limit as x approaches 0+of \sqrt[x]{x} ?
The limit as x approaches 0+of \sqrt[x]{x} is 0