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

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

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

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

e

Decimal

2.71828 \dots

Solution steps

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

Apply the common limit:

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

= e

f (x) = (4 x - x^{2})^{3}

e^{x}, x^{2} - 1, - 1.14776, 2

\int \frac{6 x + 15}{2 x + 1} d x

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{3})

2 π

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