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

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

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limit as x approaches 0+of (2x)^x

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

1

Solution steps

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

Simplify

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

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

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

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

= 1 \cdot 1

Simplify

= 1

x \to \frac{π}{2} lim (\frac{1}{tan ( x )})

x \to - 6 lim (\frac{x}{x + 6})

x \to \frac{1}{2} lim (x tan (π x))

x \to - \infty lim (x, - 3)

x \to 0 + lim (x^{l n (x)})

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