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