2018 l hopital s rule
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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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2018 L’Hopital’s Rule

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2018 l hopital s rule

2018 L’Hopital’s Rule

BC Calculus


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


Extra proof l hopital s rule

EXTRA: Proof L’Hopital’s Rule


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 ∞


Repeated use of l hopital s

Repeated use of L’Hopital’s:

EX:

By L’Hopital


2018 l hopital s rule

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:


Converting to l hopital s forms

Converting to L’Hopital’s forms:

EX:


Converting to l hopital s forms1

Converting to L’Hopital’s forms:

EX:


Converting to l hopital s forms2

Converting to L’Hopital’s forms:

EX:


Converting to l hopital s forms3

Converting to L’Hopital’s forms:

EX:


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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