Download Presentation
## 2018 L’Hopital’s Rule

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**2018 L’Hopital’s Rule**BC Calculus**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 !**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**Does it Work?**before Leading term test By L’Hopital = before = By L’Hopital**L’Hopital’s Babies**EX: EX: By L’Hopital By L’Hopital Which grows faster? Bottom goes to 0 Top goes to ∞**Repeated use of L’Hopital’s:**EX: By L’Hopital**Repeated use of L’Hopital’s:**By L’Hopital By L’Hopital**L’Hopital’s Rule**Other Indeterminant Forms: << Rem: LIMITS not values! >> Convert to L’Hopital’s forms Known Limits:**Summary:**L’Hopital ‘s Forms: Converting: Multiplication: Subtraction: Exponential: Other Properties:**Last Update:**• 11/22/11 • Assignment: p. 450 # 1- 23 odd**Turkey Quiz !**• Find the Limit: 1) 2) 3)