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

\frac{d}{d x} (25 x^{3} - 6 x^{2} + 7 x - 88)

\frac{d y}{d x} = 0.1 y (1 - \frac{y}{500})

9 y^{^{''}} - 24 y^{^{'}} + 16 y = 0

y = \frac{1}{( x ^{2} - 2 ) ( x ^{2} + x + 5 )}

y = 5 x cos (x), (π, - 5 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