   Chapter 3.4, Problem 45E

Chapter
Section
Textbook Problem

# Find a formula for a function / that satisfies the following conditions: lim x →   ± ∞ f ( x ) = 0 ,     lim x →   0 f ( x ) = − ∞ ,     f ( 2 ) = 0 , lim x →   3 − f ( x ) = ∞ ,     lim x →   3 + f ( x ) = − ∞

To determine

To find:

Formula for a function f that satisfies the given conditions

Explanation

1) Concept:

Use definition of horizontal and vertical asymptote.

2) Definitions:

Horizontal asymptote:

Horizontal asymptote:y=b

As x±, yb or limx±∞ f(x)=b

Vertical asymptote:

Vertical asymptote: x=c

As xc, y± or limxcf(x)=±

3) Given:

i. limx±fx=0

ii. limx0fx=-

iii. f2=0

iv. limx3-fx=

v. limx3+fx=-

4) Calculation:

limx±fx=0

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