We explore functions whose graphs approach a nonhorizontal line as x . A line y =

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We explore functions whose graphs approach a nonhorizontal line as x → ∞. A line y = ax + b is called a slant asymptote if

or lim (f(x) (ax+b)) = 0 X-00 lim (f(x) (ax + b)) = 0 X--0

If ƒ(x) = P(x)/Q(x), where P and Q are polynomials of degrees m + 1 and m, then by long division, we can write

f(x) = (ax + b) + P(x)/Q(x)

where P1 is a polynomial of degree

(a) y = Tou zx x + 2 (b) y = x + x x + x + 1

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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