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AP Calculus BC Wednesday, 05 March, 2014

AP Calculus BC Wednesday, 05 March, 2014. OBJECTIVE TSW (1) recognize limits that produce indeterminate forms, and (2) apply L'Hôpital’s Rule to evaluate limits. ASSIGNMENT DUE Sec. 8.5: p. 559 (1, 5-15 odd )  black tray ASSIGNMENTS DUE MONDAY WS The Logistics Curve

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AP Calculus BC Wednesday, 05 March, 2014

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  1. AP Calculus BCWednesday, 05 March, 2014 • OBJECTIVE TSW (1) recognize limits that produce indeterminate forms, and (2) apply L'Hôpital’s Rule to evaluate limits. • ASSIGNMENT DUE • Sec. 8.5: p. 559 (1, 5-15 odd)  black tray • ASSIGNMENTS DUE MONDAY • WS The Logistics Curve • Sec. 8.7: p. 574 (11-35 odd, 37-51 odd omit part C) • REMINDERS • PI Day: Friday, 14 March 2014

  2. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule

  3. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate:

  4. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate: Limit is going to infinity, degrees of numerator and denominator are the same, so look at the leading coefficients.

  5. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate:

  6. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule

  7. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Two important points to remember using L'Hôpital's Rule: (1) The Rule only applies to quotients! (2) You're finding limits, not derivatives!

  8. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Indeterminate form Ex: Evaluate: Direct substitution yields: Before you apply L’Hopital’s Rule, you must (1) show the indeterminate form and (2) explicitly state that it is indeterminate.

  9. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Examples of indeterminate forms: L'Hôpital's Rule may be used only with these indeterminate forms. L'Hôpital's Rule may NOT be used with indeterminate forms like this.

  10. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate: Indeterminate You MUST show the indeterminate form – and state that it is indeterminate – before you use L'Hôpital's Rule!

  11. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate: Indeterminate Indeterminate

  12. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate: This is not in a form to use L'Hôpital's Rule, so rewrite it: Indeterminate

  13. Sec. 8.7: Indeterminate Forms and L’Hôpital’s Rule Ex: Evaluate: Rewrite to fit a usable indeterminate form: Indeterminate Indeterminate

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