   Chapter 3.5, Problem 47E

Chapter
Section
Textbook Problem

# 45–48 Find an equation of the slant asymptote. Do not sketch the curve. y = 2 x 3 − 5 x 2 + 3 x x 2 − x − 2

To determine

To find:

An equation of the slant asymptote.

Explanation

1) Concept:

Find the equation of slant asymptote by 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=2x3-5x2+3xx2-x-2

4) Calculation:

Now find the equation of slant asymptote by long division method

Therefore,

y=2x3-5x2+3xx2-x-2

Simplified to

y=2x-3+4x-6x2-x-2

So write y=

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