Problem

Use the guidelines of this section to sketch the …

04:59

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} $

Answer

$y=-3 x+1$

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Discussion

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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?

Jamie M.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Top Calculus 2 / BC Educators

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham

Joseph L.

Boston College