Chapter 12.4, Problem 72E

To determine

To create: A table to verify that $\underset{x\to \infty }{\lim }\frac{1}{x}=0$ and make a conjecture about $\underset{x\to 0}{\lim }\frac{1}{x}$ .

Answer to Problem 72E

For $\underset{x\to -\infty }{\lim }\frac{1}{x}=0$ ,

x	-10000	-1000	-100	-10
f(x)	-0.0001	0.001	-0.010	-0.100

For $\underset{x\to \infty }{\lim }\frac{1}{x}=0$ ,

x	10	100	1000	10000
f(x)	0.100	0.010	0.001	0.0001

The conjecture about $\underset{x\to 0}{\lim }\frac{1}{x}=0$

Explanation of Solution

Given information:

  $\underset{x\to \infty }{\lim }\frac{1}{x}=0$

  $\underset{x\to 0}{\lim }\frac{1}{x}$

Calculation:

For $\underset{x\to -\infty }{\lim }\frac{1}{x}=0$ ,

x	-10000	-1000	-100	-10
f(x)	-0.0001	0.001	-0.010	-0.100

For $\underset{x\to \infty }{\lim }\frac{1}{x}=0$ ,

x	10	100	1000	10000
f(x)	0.100	0.010	0.001	0.0001

The conjecture about $\underset{x\to 0}{\lim }\frac{1}{x}=0$

Thus we can create a table to verify the given limit and make a conjecture.