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Applied Calculus (MAT 121) Dr. Day Thursday Feb 23, 2012

Applied Calculus (MAT 121) Dr. Day Thursday Feb 23, 2012. Return to “the limit” As the inputs approach some value, is there a recognizable pattern of approachment in the output values? Vertical Asymptotes: Denominator Issues? Horizontal Asymptotes: x  ∞ , x  −∞.

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Applied Calculus (MAT 121) Dr. Day Thursday Feb 23, 2012

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  1. Applied Calculus (MAT 121)Dr. Day Thursday Feb 23, 2012 • Return to “the limit” • As the inputs approach some value, is there a recognizable pattern of approachment in the output values? • Vertical Asymptotes: Denominator Issues? • Horizontal Asymptotes: x∞, x−∞ MAT 121

  2. Recall: Determining Limits • Calculate: How calculate limits? Try subbing in value! Simplify if possible and return to (a). Use a numerical approach: Sub in values closer and closer to the limiting input value. Look at a graph of the function and visualize the limit. Play the S & S Game: Identify SIZE and SIGN MAT 121

  3. Vertical Asymptotes • Use Results: MAT 121

  4. Horizontal Asymptotes • Use Results: MAT 121

  5. Horizontal and Vertical Asymptotes Example: Determine all horizontal and vertical asymptotes for the function MAT 121

  6. Putting It All Together: Curve Sketching Example: Sketch a graph of the function. Do not show graph on your calculator! MAT 121

  7. Putting It All Together: Curve Sketching MAT 121

  8. Assignments WebAssign 4.2 due tonight. 4.3 due Monday night. Quiz #4 now open! MAT 121

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