Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
(a) limx➔oo x 3 = oo (b) limx➔-oo x 3 = -oo (c) limx➔-oo x 4 = oo
Expert Solution
Step 1: (a)
To check limit of x3 as x→∞
To construct a table by taking larger values of x and finding corresponding values of x3
| x | x3 |
| -1 | -1 |
| -100 | -100000 |
| -1000 | -1000000000 |
| -10000 | -1012 |
| -1000000 | -1018 |
| -1010 | -1030 |
| 1010 | 1030 |
| 1000000 | 1018 |
| 1000 | 1012 |
| 100 | 1000000 |
| 1 | 1 |
Step 2
From the table, draw a graph of x3
From the graph, as x increases x3 also increases.
That means as x tends to ∞, the graph is going up and increases without bound.
Therefore,
Step 3(b)
To show,
Construct the table to find limit of x4 as x→-∞
| x | x3 |
| -1 | -1 |
| -100 | -100000 |
| -1000 | -1000000000 |
| -10000 | -1012 |
| -1000000 | -1018 |
| -1010 | -1030 |
| 1010 | 1030 |
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