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Calculus / Calculus: Early Transcendentals 9 / Chapter 2.6 / Problem 66

Calculus: Early Transcendentals | 9th Edition | ISBN: 9781337613927 | Authors: Daniel K. Clegg, Saleem Watson, James Stewart

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?End Behavior of a Function By the end behavior of a function we mean the behavior of

Chapter 2, Problem 66

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QUESTION:

End Behavior of a Function By the end behavior of a function we mean the behavior of its values as $x→∞$ and as $x→-∞$ .
(a) Describe and compare the end behavior of the functions

$P(x)=3{x}^{5}-5{x}^{3}+2x\ Q(x)=3{x}^{5}$

by graphing both functions in the viewing rectangles $[-2,2]$ by $[-2,2]$ and $[-10,10]$ by $[-10,000,10,000]$ .

(b) Two functions are said to have the same end behavior if their ratio approaches 1 as $x→∞$ , Show that $P$ and $Q$ have the same end behavior.

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QUESTION:

End Behavior of a Function By the end behavior of a function we mean the behavior of its values as $x→∞$ and as $x→-∞$ .
(a) Describe and compare the end behavior of the functions

$P(x)=3{x}^{5}-5{x}^{3}+2x\ Q(x)=3{x}^{5}$

by graphing both functions in the viewing rectangles $[-2,2]$ by $[-2,2]$ and $[-10,10]$ by $[-10,000,10,000]$ .

(b) Two functions are said to have the same end behavior if their ratio approaches 1 as $x→∞$ , Show that $P$ and $Q$ have the same end behavior.

ANSWER:

Step 1 of 3

The given functions are and .

We were asked to draw viewing rectangles of above functions by , and by .

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