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Limits: Evaluation TechniquesPowerPoint Presentation

Limits: Evaluation Techniques

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Limits: Evaluation Techniques

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Limits: Evaluation Techniques

2.3

-1

Multiply by LCD

Cancel

(4)

Substitute and Solve

-1

Multiply by LCD

Cancel

(2)

Substitute and Solve

Use piecewise definition for absolute value functions

Limit DNE!

Use piecewise definition for absolute value functions

Limit DNE!

Cancel

Substitute and Solve

64

16

Rewrite as a single fraction using LCD

D.S -> 0/0

Rationalize Numerator

-1

Simplify

Cancel

0

0

Substitute and solve

TRIG

LIMITS

=1

Must match exactly!

=0

Must match exactly

EXAMPLES

Multiply numerator and denominator by 3

Since they match…let’s use our theorem

Property of Limits

Trapped between: This makes a limit sandwich!

0

0

By Squeeze Theorem