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 transcript:

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 first 2 seconds of fall? Need to know: Find the average speed from 2 seconds to slightly past 2 seconds…

INSTANTANEOUS RATE OF CHANGE

TYPES OF LIMITS Graph.

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”.

BEHAVIOR OF A LIMIT

PROPERTIES OF LIMITS

USE SUBSTITUTION FIRST!!! USE FACTORING SECOND SIMPLIFY THIRD

Show graph…show numerically…compare answersnumerically

USE PRODUCT RULE

LEFT AND RIGHT LIMITS

FIND THE LIMITS Homework : Interact Math.com lesson 2.1