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

\frac{d}{d x} ((5 x^{2} + 3) (4 x - 3))

\frac{d}{d x} (14 x e^{x})

\frac{\partial}{\partial x} (4 ln (x + z))

\int (x + 5) (x - 3) d x

\frac{d}{d x} (2 e^{c o s (x)})

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