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 Notation

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

y = 3 e^{- x}, (0, 3)

\frac{d y}{d x} + \frac{3 x y}{x ^{2} + 1} = \frac{6 x}{x ^{2} + 1}

\int \frac{1}{4 + 8 x} d x

\int 7 x^{\frac{2}{5}} + 3 x^{- \frac{4}{5}} d x

y^{^{'''}} - 5 y^{^{''}} + 3 y^{^{'}} + 9 y = 0

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