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

The limit as x approaches 0 of (1+x)^x is 1

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limit as x approaches 0 of (1+x)^x

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

1

Solution steps

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

Plug in the value

x = 0

= (1 + 0)^{0}

Simplify

= 1

\frac{\partial}{\partial x} (x y e^{3 y})

\frac{d}{d x} (10 x^{\frac{1}{5}})

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

x^{\frac{11}{2}}, x = 1

f (x) = - 3 x^{\frac{3}{2}} - 1, at x = 4

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