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

The limit as x approaches 2 of (1+1/x)^x is 9/4

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

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

\frac{9}{4}

Decimal

2.25

Solution steps

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

Plug in the value

x = 2

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

Simplify

(1 + \frac{1}{2})^{2} : \frac{9}{4}

= \frac{9}{4}

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What is the limit as x approaches 2 of (1+1/x)^x ?
The limit as x approaches 2 of (1+1/x)^x is 9/4