   Chapter 3.5, Problem 48E

Chapter
Section
Textbook Problem

# 45–48. Find an equation of the slant asymptote. Do not sketch the curve. y = − 6 x 4 + 2 x 3 + 3 2 x 3 − x

To determine

To find:

An equation of the slant asymptote

Explanation

1) Concept:

Find the equation of slant asymptote by the long division method

2) Definition:

Slant asymptote: the line y=mx+b is called a slant asymptote if

limx±fx-(mx+b)=0

3) Given:

y=-6x4+2x3+32x3-x

4) Calculation:

Now find the equation of slant asymptote by using long division method

Therefore,

y=-6x4+2x3+32x3-x

Simplified to

y=-3x+1+-3x2+x+32x3

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