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

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

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limit as x approaches 0+of (x)^{3x}

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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

x \to 0 lim (x cos (3 x))

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

x \to - \infty lim (- 6)

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

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