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1 Ch. 1 Limits and Their Properties 1.1

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  • 1

    Ch. 1 Limits and Their Properties

    1.1                                                                                          

                                                                        

                                                                     

  • 2

    What is

    Calculus?!!

                   -              

                       (                   ! ) 

  • 3

    Branches of Calculus (2)

                                       ,              ,                 .

                         

                     

    1.                                    !2.                     !

                        (        /     )                                    !.

    1.                2.                           

  • 4

                            :

                  

                

                                         !

            

    "static" "dynamic!"

    (see p43 and 44)

                        . . .          !

                           

    1.

    +             2.        3.

  • 5

                                                                        !

                               

                               

                                 

                      

                       FEATURES

    AnimationTangent Line [2.1]

  • 6

    x

    y

  • 7

    x

    y

  • 8

    x

    y

  • 9

    x

    y

  • 10

    msec= f (c +   x)  f (c) (c +   x)  c     x=

    f (c +   x)  f (c)

                         ,xmsec=mtangent limit as  0

  • 11

                    (Exact) Area 

    Under the Curve

    = limit Area rectanglesas n

                       46

                    46

  • 12

    x

    y

  • 13

    x

    y

  • 14

    x

    y

  • 15

                   :          1.1Coordinate Plane Distance;                The Distance Formula

    The distance between P1(x1, y1) and P2(x2, y2) is:

    d= (x2  x1)2 + (y2  y1)2

    Geometry Formulas#8. Vcylinder= r2 h

  • 16

    Assignment

    p 47 #1-11 all

  • Attachments

    calc7emain.html

    SMART Notebook

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