AKA, Asymptotes of Rational Functions, Calculus Style

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Presentation transcript:

AKA, Asymptotes of Rational Functions, Calculus Style Limits and Infinity AKA, Asymptotes of Rational Functions, Calculus Style

Part I: Infinite Limits: vertical asymptote at x=0. online.math.uh.edu/HoustonACT/Greg_Kelly.../Calc02_2.ppt

“On the contrary, it tells HOW the limit FAILS to exist.” IMPORTANT NOTE: The equal sign in the statement does NOT mean the limit exists! “On the contrary, it tells HOW the limit FAILS to exist.” Page 80 Dr. Larson & Dr. Hostetler www.vcsc.k12.in.us/lincoln/math/CaseNotes/.../InfiniteLimits.ppt

Definition of a Vertical Asymptote If f(x) approaches infinity or negative infinity as x approaches c from the left or right, then x = c is a vertical asymptote of f. www.vcsc.k12.in.us/lincoln/math/CaseNotes/.../InfiniteLimits.ppt

Digging deeper… Infinity is a very special idea. We know we can't reach it, but we can still try to work out the value of functions that have infinity in them. http://www.mathsisfun.com/calculus/limits-infinity.html

Question: What is the value of 1/∞ ? Answer: We don't know! Maybe we could say that 1/∞ = 0, ... but if we divide 1 into infinite pieces and they end up 0 each, what happened to the 1? In fact 1/∞ is known to be undefined. http://www.mathsisfun.com/calculus/limits-infinity.html

But We Can Approach It! x 1/x 1 1.00000 2 0.50000 4 0.25000 10 0.10000 0.01000 1,000 0.00100 10,000 0.00010 http://www.mathsisfun.com/calculus/limits-infinity.html

The limit of 1/x as x approaches Infinity is 0 Furthermore: http://www.mathsisfun.com/calculus/limits-infinity.html

Limits at Infinity Divide through by the highest power of x Simplify Substitute 0 for 1/xn www.mrsantowski.com/MCB4U/Notes/PowerPointNotes/BCC016.ppt

Example Divide by www.rowan.edu/open/depts/math/.../Limits%20and%20Continuity.pp.

More Examples www.rowan.edu/open/depts/math/.../Limits%20and%20Continuity.pp.

www.rowan.edu/open/depts/math/.../Limits%20and%20Continuity.pp.

Worksheet Review: Page 91, Homework Worksheet Review: Page 91, #3-5, 11-18, 27-30, 41, 42, 44, 47, 49, 50, 55, 59-61, 63-64