What is the limit as x approaches 3 of (1/2+1/x)^x ?

The limit as x approaches 3 of (1/2+1/x)^x is 125/216

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limit as x approaches 3 of (1/2+1/x)^x

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

\frac{125}{216}

Decimal

0.57870 \dots

Solution steps

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

Plug in the value

x = 3

= (\frac{1}{2} + \frac{1}{3})^{3}

Simplify

(\frac{1}{2} + \frac{1}{3})^{3} : \frac{125}{216}

= \frac{125}{216}

x \to 3 lim (\frac{1}{x - 1})

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What is the limit as x approaches 3 of (1/2+1/x)^x ?
The limit as x approaches 3 of (1/2+1/x)^x is 125/216