What is the limit as x approaches 0+of x^{3x^2} ?

The limit as x approaches 0+of x^{3x^2} is 1

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limit as x approaches 0+of x^{3x^2}

x \to 0 + lim (x^{3 x^{2}})

1

Solution steps

x \to 0 + lim (x^{3 x^{2}})

Apply exponent rules

= x \to 0 + lim (e^{3 x^{2} l n (x)})

Apply the Limit Chain Rule:

1

= 1

x \to 1 lim (\frac{5 ln ( x )}{x})

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

x \to 2 lim (\frac{3 x + 5}{x - 2})

x \to 3 + lim (\frac{1}{9 - x ^{2}})

x \to 4 lim (- x^{2} + 2 x + 2)

What is the limit as x approaches 0+of x^{3x^2} ?
The limit as x approaches 0+of x^{3x^2} is 1