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

The limit as x approaches 0+of (2x)^{3x} is 1

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

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

1

Solution steps

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

Simplify

(2 x)^{3 x} : 8^{x} x^{3 x}

= x \to 0 + lim (8^{x} x^{3 x})

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

With the exception of indeterminate form

= x \to 0 + lim (8^{x}) \cdot x \to 0 + lim (x^{3 x})

x \to 0 + lim (8^{x}) = 1

x \to 0 + lim (x^{3 x}) = 1

= 1 \cdot 1

Simplify

= 1

y = \frac{x ^{2} - 1}{x ^{2} + x + 1}

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

\frac{\partial}{\partial x} (- 4 cos (x))

x \to 1 lim (4 x - 5)

\frac{\partial}{\partial z} (x y e^{yz})

What is the limit as x approaches 0+of (2x)^{3x} ?
The limit as x approaches 0+of (2x)^{3x} is 1