   Chapter 3.4, Problem 62E

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 functions P ( x ) = 3 x 5 − 5 x 3 + 2 x     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.

To determine

a) To describe:

To describe the end behavior of the given functions

Explanation

1) Given:

Px=3x5-5x3+2x and  Qx=3x5

2) Calculation:

Description of end behavior: The given functions has infinite range

limxPx= limxQx=

limx-Px=-

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