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Problem

Use the guidelines of this section to sketch the …

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Problem 64 Medium Difficulty

Find an equation of the slant asymptote. Do not sketch the curve.

$ y = \dfrac{-6x^4 + 2x^3 + 3}{2x^3 - x} $


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Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Related Topics

Derivatives

Differentiation

Volume

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Watch More Solved Questions in Chapter 4

Problem 1
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Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
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Problem 13
Problem 15
Problem 16
Problem 17
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Problem 25
Problem 26
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Problem 28
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Problem 37
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Problem 76

Video Transcript

So, um, to find the slant ass. Until for this one, we're going to do polynomial division. So, um, how many times can to x cube go into negative six x to the fourth? So we're gonna do minus three x. So minus three X sometimes two x to the third. Normally would be, ah, negative. Six extra before they were gonna changes. Sign for everything in this row so that we can cancel out the first term. So plus six x to the fourth next term, a minus three x squared. Okay, so now we're gonna cancel the first term, and we're gonna be left with, um two x cubed a minus three x squared, plus three. Don't forget to drop the three. Next we have How many times can to x cubed going to two x cubed exactly once. Um, so one times two x cubed. And then remember, change science. So minus two x cubed plus X. So cancels out the first term. And then we're left with minus three x squared plus X plus three as our remainder. And we know so remainder because the power of two x cubed is larger. Um, the power of two x cubed is larger than the power of negative three x two second power. Okay, so this is our quotient. And it is also our slant ass into So why equals minus three x post one? Is this land as in two for this function?

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Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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