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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.

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Presentation Transcript
finding limits
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 !

l hopital s rule

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
Does it Work?

before

Leading term test

By L’Hopital

=

before

=

By L’Hopital

l hopital s babies
L’Hopital’s Babies

EX:

EX:

By L’Hopital

By L’Hopital

Which grows faster?

Bottom goes to 0

Top goes to ∞

slide8

Repeated use of L’Hopital’s:

By L’Hopital

By L’Hopital

l hopital s rule1
L’Hopital’s Rule

Other Indeterminant Forms: << Rem: LIMITS not values! >>

Convert to L’Hopital’s forms

Known Limits:

summary
Summary:

L’Hopital ‘s Forms:

Converting:

Multiplication:

Subtraction:

Exponential:

Other Properties:

last update
Last Update:
  • 11/22/11
  • Assignment: p. 450 # 1- 23 odd
turkey quiz
Turkey Quiz !
  • Find the Limit:

1)

2)

3)

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