What is the limit as x approaches 0 of (1+1x)^{1/x} ?

The limit as x approaches 0 of (1+1x)^{1/x} is e

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limit as x approaches 0 of (1+1x)^{1/x}

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

e

Decimal

2.71828 \dots

Solution steps

x \to 0 lim ((1 + 1 \cdot x)^{\frac{1}{x}})

Simplify

= x \to 0 lim ((1 + x)^{\frac{1}{x}})

Apply the common limit:

x \to 0 lim ((1 + x)^{\frac{1}{x}}) = e

= e

What is the limit as x approaches 0 of (1+1x)^{1/x} ?
The limit as x approaches 0 of (1+1x)^{1/x} is e