2018 L’Hopital’s Rule

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)