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

Limits: Evaluation Techniques

2.3


Find the limit

Find the Limit

-1

Multiply by LCD

Cancel

(4)

Substitute and Solve


Example

Example

-1

Multiply by LCD

Cancel

(2)

Substitute and Solve


Limits evaluation techniques

Use piecewise definition for absolute value functions

Limit DNE!


Limits evaluation techniques

Use piecewise definition for absolute value functions

Limit DNE!


Examples

Examples

Cancel

Substitute and Solve

64

16


Limits evaluation techniques

Rewrite as a single fraction using LCD

D.S -> 0/0

Rationalize Numerator

-1

Simplify

Cancel

0

0

Substitute and solve


Limits evaluation techniques

TRIG

LIMITS


Limits evaluation techniques

=1

Must match exactly!


Limits evaluation techniques

=0

Must match exactly


Limits evaluation techniques

EXAMPLES


Limits evaluation techniques

Multiply numerator and denominator by 3

Since they match…let’s use our theorem

Property of Limits


Limits evaluation techniques

Trapped between: This makes a limit sandwich!

0

0

By Squeeze Theorem


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