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Find an equation of the slant asymptote. Do not sketch the curve.
$ y = \dfrac{2x^3 - 5x^2 + 3x}{x^2 - x - 2} $
see solution
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 5
Summary of Curve Sketching
Derivatives
Differentiation
Volume
Oregon State University
Harvey Mudd College
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So the quotient of our polynomial division is going to be the equation for these slant ask himto. So, um, how many times can x square to go into two x cubed two x So two x times x squared We're gonna multiply this by every single term and change the sign because we want the 1st 1 to cancel out. So, um, we get minus two x cubed two x times negative X is two x squared negative two x squared. But we wanted to be positive because we're switching all the signs. So plus two x squared and then the last term sort to sign minus for X racing ideas to cancel out And we're left with minus three x squared minus X. So we're going to do so now we're going to do our next term. How many times can x squared going to minus three x squared? So that's minus three minus three times x squared trains The sign plus three X squared minus three X minus six and we're left with minus four X minus six. And this can. Now this one's power is greater than this. So we're done. This is our quotient. So that's the equation. Why equals two X minus three is the equation for the slants ass in tow
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