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

The limit as x approaches a of (1+1/x)^x is (1+1/a)^a

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

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

(1 + \frac{1}{a})^{a}

Solution steps

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

Plug in the value

x = a

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

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