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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Plug in the value

x = 1

= 2^{\frac{1}{1 - 2}}

Simplify

2^{\frac{1}{1 - 2}} : \frac{1}{2}

= \frac{1}{2}

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