   Chapter 2.6, Problem 66E

Chapter
Section
Textbook Problem

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 functionsP(x) = 3x5 – 5x3 + 2x Q(x) = 3x5by 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.

(a)

To determine

To describe: The end behavior of the functions P(x)=3x55x3+2x and Q(x)=3x5 by graphing.

Explanation

The polynomials P(x)=3x55x3+2x and Q(x)=3x5.

Graph:

Use the online graphing calculator and draw the graph of the functions P(x)=3x55x3+2x and Q(x)=3x5 in viewing rectangle [2,2]by [2,2] as shown below in Figure 1.

(b)

To determine

To show: The polynomials equations have the same end behavior if their ratio approaches 1 as x tends to infinity.

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