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

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

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

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

2

Solution steps

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

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

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 2 \cdot 1

Simplify

= 2

\frac{d}{d x} (\frac{1}{x ^{3} + 4 x ^{2}})

\frac{d}{d x} (x^{2} cos (x) - 2 x sin (x) - 2 cos (x))

\int 7 tan^{2} (x) + tan^{4} (x) d x

\int 3 x^{3} - 5 x^{2} + 7 x + 2 d x

\frac{d}{d x} (\frac{5 x + 1}{2 x ^{2} + 1})

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