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

The limit as x approaches 0+of 3x^{(x/2)} is 3

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

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

3

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 3 \cdot 1

Simplify

= 3

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