What is the limit as x approaches 0-of 2/(1-2^{1/x)} ?

The limit as x approaches 0-of 2/(1-2^{1/x)} is 2

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limit as x approaches 0-of 2/(1-2^{1/x)}

x \to 0 - lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})

2

Solution steps

x \to 0 - lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})

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

= 2 \cdot x \to 0 - lim (\frac{1}{1 - 2 ^{\frac{1}{x}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 2 \cdot \frac{lim _{x \to 0 -} ( 1 )}{lim _{x \to 0 -} ( 1 - 2 ^{\frac{1}{x}} )}

x \to 0 - lim (1) = 1

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

= 2 \cdot \frac{1}{1}

Simplify

= 2

x \to 2 lim (7 x^{2} + 3 x - 40)

x \to 1 lim (2^{- x} - 2^{x})

x \to 0 lim (x^{5} \cdot ln (x))

x \to 0 + lim (\frac{x}{ln ( 5 x + 1 )})

x \to \infty lim (11)

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