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

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

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

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

2

Solution steps

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

Plug in the value

x = 1

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

Simplify

= 2

x \to 4 lim (3 x + 2 + 2 x)

x \to 0 + lim (x^{- 4})

x \to - \infty lim (2^{2 x})

x \to 0 lim (\frac{\frac{1}{x}}{1})

x \to \infty lim (- 12 x^{5})

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