(a) limx➔oo x 3 = oo (b) limx➔-oo x 3 = -oo (c) limx➔-oo x 4 = oo

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...
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(a) limx➔oo x 3 = oo (b) limx➔-oo x 3 = -oo (c) limx➔-oo x 4 = oo

Expert Solution
Step 1: (a)

Calculus homework question answer, step 1, image 1

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

Calculus homework question answer, step 2, image 1

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,

Calculus homework question answer, step 2, image 2

Step 3(b)

To show,

Calculus homework question answer, step 3, image 1

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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