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2.1RATES OF CHANGE AND LIMITS LIMITS. AVERAGE SPEED=DISTANCE/TIME A rock breaks loose from the top of a tall cliff. What is the average speed during the.

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Presentation on theme: "2.1RATES OF CHANGE AND LIMITS LIMITS. AVERAGE SPEED=DISTANCE/TIME A rock breaks loose from the top of a tall cliff. What is the average speed during the."— Presentation transcript:

1 2.1RATES OF CHANGE AND LIMITS LIMITS

2 AVERAGE SPEED=DISTANCE/TIME A rock breaks loose from the top of a tall cliff. What is the average speed during the first 2 seconds of fall? Need to know: Find the average speed from 2 seconds to slightly past 2 seconds…

3 INSTANTANEOUS RATE OF CHANGE

4 TYPES OF LIMITS Graph.

5 DEFINITION OF A LIMIT Let a function “f” be defined on an open interval containing “a” except possibly itself. The statement “limit as x approaches a in the function is equal to k” means that f(x) is approaching the y-value of “k” as x gets sufficiently close to “a”.

6 BEHAVIOR OF A LIMIT

7 PROPERTIES OF LIMITS

8 USE SUBSTITUTION FIRST!!! USE FACTORING SECOND SIMPLIFY THIRD

9 Show graph…show numerically…compare answersnumerically

10 USE PRODUCT RULE

11 LEFT AND RIGHT LIMITS

12

13 FIND THE LIMITS Homework : Interact Math.com lesson 2.1

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