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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 ( 1 + 1 x ) x , with a decimal expansion beginning 2.7182818284590452353602874713527... . It is an important number in calculus, defined so that the slope of the line tangent to f ( x ) = e x at ( 0 , 1 ) is equal to 1 .

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

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