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# 1.E Exercises

• Page ID
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}$$?

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

Exercise $$\PageIndex{2}$$

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