Calculus Question

Question

Find the oblique asymptote for the graph of y = x³/x²-x.

Help!?

Answer 1

If you divide out   x³ / (x² - x)   OR    x² / (x - 1)

  [ Simplify by factoring to get   x³ / x (x - 1) = x² / (x - 1) ]

You will get   x + 1  + 1/(x - 1)

As x goes to ∞ the last term disappears to 0 and the

OA is  y = x + 1

 

 

Answer 2

Assuming that you intended the denominator to be (x²-x) [ otherwise your function simplifies to zero ], it does meet the condition for having an oblique (or 'slant') asymptote.

 

Divide and discard the remainder term; you get y = x+1 as the equation of the O.A.

Answer 3

x³ / x² = x

y = x