1.5 LIMITS Calculus 9/16/14. WARM-UP LIMITS – P. 49.

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Presentation transcript:

1.5 LIMITS Calculus 9/16/14

WARM-UP

LIMITS – P. 49

GOAL Find limits graphically or numerically Use properties of limits and analytic techniques to evaluate limits of a function

DEFINITION

FINDING A LIMIT

EX. 1

EXAMPLE 2. Graph

EXAMPLE 3 Graph

EX. 3 Graph

FIND THE LIMIT

PROPERTIES –P.51

OPERATIONS

EX 6- FIND THE LIMIT

WARM-UP

LIMTS Limits are useful when we need to find the value of a function getting close to a certain “x” value We can use direct substitution (“plug in” the x to find the value at that point), but sometimes that is not possible and limits help us see what the function value could be as we approach that x value

FIND THE LIMIT

ONE- SIDED LIMITS

DOES THE LIMIT EXIST OR NOT?

FIND A ONE-SIDED LIMIT

UNBOUNDED BEHAVIOR

COMPARING ONE SIDED LIMITS Ex. 9 in the book.