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2018 L’Hopital’s Rule

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2018 L’Hopital’s Rule

BC Calculus

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 )

CAUTION: Think of this as the comparison of two functions

NOT a Quotient Rule << NOT Bo-d(To) >>

IE> and

before

Leading term test

By L’Hopital

=

before

=

By L’Hopital

EX:

EX:

By L’Hopital

By L’Hopital

Which grows faster?

Bottom goes to 0

Top goes to ∞

EX:

By L’Hopital

Repeated use of L’Hopital’s:

By L’Hopital

By L’Hopital

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

Convert to L’Hopital’s forms

Known Limits:

EX:

EX:

EX:

EX:

L’Hopital ‘s Forms:

Converting:

Multiplication:

Subtraction:

Exponential:

Other Properties:

- 11/22/11
- Assignment: p. 450 # 1- 23 odd

- Find the Limit:
1)

2)

3)