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

y = 3 x, y = 9 x^{2}

y^{^{''}} + 4 y = 9 e^{2 t} sin (2 t) + 5 t^{2}

sec (x)

x \to 0 lim (arctan (x))

\frac{s - 1}{s ^{2} - 2 s + 1}

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