   Chapter 3.4, Problem 35E

Chapter
Section
Textbook Problem

# 35-40 Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. y = 5 + 4 x x + 3

To determine

To find:

The horizontal and vertical asymptotes and check the work by graphing the curve and estimating asymptotes.

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:

y=5+4xx+3

4) Calculation:

Consider the given function,

y=5+4xx+3

Divide numerator and denominator by x and by using limit properties find the limit

limx5+4xx+3

=limx5+4xxx+3x

Simplify,

=limx5x+41+3x

Apply limit separately,

=limx5x+limx4limx1+limx3

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