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Mathematics LibreTexts

1.1E: Exercises

  • Page ID
    11018
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    Exercise \(\PageIndex{1}\): Euler number

    Consider the function \(f(x)=\left(1+\dfrac{1}{x}\right)^x\). Make a table showing \(f(x)\) for \(x=1,2,3, .....\) . Round your solutions to five decimal places. What can you say about the value of the function \(f(x)\) as \(x\) increases indefinitely?

    Answer

    \(\lim_{x \to \infty}\left(1+\dfrac{1}{x}\right)^x=2.7183=e.\)