# Limits: Evaluation Techniques - PowerPoint PPT Presentation

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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