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

\int e^{- 2 x} x d x

\frac{\partial}{\partial x} (x^{4} y^{8} + 4 x^{5} y)

ln (\frac{x}{x ^{2} + 2})

\frac{d}{d x} (5 lo g_{2} (x))

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

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