What is the limit as x approaches 0+of (2x)^{5x} ?

The limit as x approaches 0+of (2x)^{5x} is 1

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limit as x approaches 0+of (2x)^{5x}

x \to 0 + lim ((2 x)^{5 x})

1

Solution steps

x \to 0 + lim ((2 x)^{5 x})

Simplify

(2 x)^{5 x} : 3 2^{x} x^{5 x}

= x \to 0 + lim (3 2^{x} x^{5 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 (3 2^{x}) \cdot x \to 0 + lim (x^{5 x})

x \to 0 + lim (3 2^{x}) = 1

x \to 0 + lim (x^{5 x}) = 1

= 1 \cdot 1

Simplify

= 1

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What is the limit as x approaches 0+of (2x)^{5x} ?
The limit as x approaches 0+of (2x)^{5x} is 1