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Mathematics LibreTexts

1.E Exercises

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    10247
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    1.1 

    Exercise \(\PageIndex{1}\) Euler number 

    Consider the function \(f(x)=(1+\dfrac{1}{x})^x\). Make a table showing the values of f for \(x=−0.01,−0.001,−0.0001,−0.00001\) and for \(x=0.01,0.001,0.0001,0.00001\). Round your solutions to five decimal places.

    \(x\) \(f(x)\) \(x)\ \(f(x)\)
    -0.01 a. 0.01 e.
    -0.001 b. 0.001 f.
    -0.0001 c. 0.0001 g.
    -0.00001 d. 0.00001 h.
    1. What does the table of values in the preceding exercise indicate about the function \(f(x)=(1+x)^{1/x}\)?
     
    Answer:

    \(\lim_{x \to 0}(1+x)^{1/x}=2.7183\)

     

     

     

    Exercise \(\PageIndex{2}\)

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