2018 L’Hopital’s Rule - PowerPoint PPT Presentation

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2018 L’Hopital’s Rule

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  1. 2018 L’Hopital’s Rule BC Calculus

  2. FINDING LIMITS Rem: Always start with Direct Substitution Method 1: Algebraic - Factorization Method 2: Algebraic - Rationalization Today is the Day!!! Method 3: Numeric – Chart (last resort!) Method 4: Calculus To be Learned Later !

  3. If produces the Indeterminant Form,( or ), then Provided the limit exists and . (Also ) L’Hopital’s Rule CAUTION: Think of this as the comparison of two functions NOT a Quotient Rule << NOT Bo-d(To) >> IE> and

  4. EXTRA: Proof L’Hopital’s Rule

  5. Does it Work? before Leading term test By L’Hopital = before = By L’Hopital

  6. L’Hopital’s Babies EX: EX: By L’Hopital By L’Hopital Which grows faster? Bottom goes to 0 Top goes to ∞

  7. Repeated use of L’Hopital’s: EX: By L’Hopital

  8. Repeated use of L’Hopital’s: By L’Hopital By L’Hopital

  9. L’Hopital’s Rule Other Indeterminant Forms: << Rem: LIMITS not values! >> Convert to L’Hopital’s forms Known Limits:

  10. Converting to L’Hopital’s forms: EX:

  11. Converting to L’Hopital’s forms: EX:

  12. Converting to L’Hopital’s forms: EX:

  13. Converting to L’Hopital’s forms: EX:

  14. Summary: L’Hopital ‘s Forms: Converting: Multiplication: Subtraction: Exponential: Other Properties:

  15. Last Update: • 11/22/11 • Assignment: p. 450 # 1- 23 odd

  16. Turkey Quiz ! • Find the Limit: 1) 2) 3)