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The Number $e$

The number, $e$ , is an irrational number defined as the limit of $x$ as $x$ approaches infinity of ${\left(1+\frac{1}{x}\right)}^x$ , with a decimal expansion beginning $\mathrm{2.7182818284590452353602874713527...}$ . It is an important number in calculus, defined so that the slope of the line tangent to $f\left(x\right)=e^x$ at $\left(0,1\right)$ is equal to $1$ .

Because $f\left(x\right)=e^x$ has special calculus properties that simplify many calculations, it is considered the natural exponential function .