What is the limit as x approaches 0+of x^{x/3} ?

The limit as x approaches 0+of x^{x/3} is 1

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limit as x approaches 0+of x^{x/3}

x \to 0 + lim (x^{\frac{x}{3}})

1

Solution steps

x \to 0 + lim (x^{\frac{x}{3}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{x}{3} l n (x)})

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (\frac{6 x}{cot ( x )})

x \to - 1 lim (3 x (2 x - 1))

x \to 3 lim ((x - 3) (x - 4))

x \to 3 lim (2 x^{2} - 7)

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

What is the limit as x approaches 0+of x^{x/3} ?
The limit as x approaches 0+of x^{x/3} is 1