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

The limit as x approaches 2 of (1+x)^{1/x} is 3^{1/2}

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

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

3^{\frac{1}{2}}

Solution steps

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

Plug in the value

x = 2

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

Simplify

= 3^{\frac{1}{2}}

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