Limits evaluation techniques
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Limits: Evaluation Techniques. 2.3. Find the Limit. -1. Multiply by LCD. Cancel. (4). Substitute and Solve. Example. -1. Multiply by LCD. Cancel. (2). Substitute and Solve. Use piecewise definition for absolute value functions. Limit DNE!.

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Limits: Evaluation Techniques

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Limits: Evaluation Techniques

2.3


Find the Limit

-1

Multiply by LCD

Cancel

(4)

Substitute and Solve


Example

-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!


Examples

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


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