
1.1E Exercises

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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?

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