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File: Calculus Pdf 168662 | Ap Calculus Ab Notes
ap calculus ab notes 20182019 arbor view hs name period 1 table of contents 1 2 finding limits graphically and numerically 48 4 1 3 evaluating limits analytically 57 7 ...

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                AP Calculus AB 
                              
             Notes 2018‐2019 
                              
                              
                Arbor View HS 
                              
                              
         Name:                                    
                              
                       Period:      
                              
      
                                                    1 
      
     Table of Contents 
     1.2 Finding Limits Graphically and Numerically (48)................................................................................... 4 
     1.3 Evaluating Limits Analytically (57) ........................................................................................................ 7 
     1.4 Continuity and One-Sided Limits (68) ................................................................................................... 10 
     1.5 Infinite Limits (80) ................................................................................................................................. 14 
     3.5 Limits at Infinity (192) ........................................................................................................................... 18 
     2.1 The Derivative and the Tangent Line Problem (94) .............................................................................. 20 
     2.2 Basic Differentiation Rules (105) .......................................................................................................... 23 
     2.2 Day 2 Rates of Change (109) ................................................................................................................. 26 
     2.3 Product and Quotient Rules (117) .......................................................................................................... 29 
     2.3 Day 2 Trigonometric & Higher-Order Derivatives (121) ...................................................................... 32 
     2.4 Day 1 Chain Rule (127) ......................................................................................................................... 36 
     2.4 Day 2 Chain Rule (132) ......................................................................................................................... 39 
     2.5 Day 1 Implicit Differentiation (132) ...................................................................................................... 42 
     2.5 Day 2 Implicit Differentiation (132) ...................................................................................................... 45 
     2.6 Day 1 Related Rates (144) ..................................................................................................................... 47 
     2.6 Day 2 Related Rates (144) ..................................................................................................................... 50 
     3.1 Extrema on an Interval (160) ................................................................................................................. 53 
     3.2 Rolle’s & Mean Value Theorems (168) ................................................................................................. 55 
     3.3 Increasing/Decreasing f(x)s and the 1st Derivative Test (174) .............................................................. 58 
     3.4 Concavity and the 2nd Derivative Test (184) ........................................................................................ 61 
     3.6 Summary of Curve Sketching (202) ...................................................................................................... 64 
     3.7 Optimization (211) ................................................................................................................................. 68 
                                               2 
      
     3.8 Newton’s Method (222) ......................................................................................................................... 72 
     3.9 Differentials (228) .................................................................................................................................. 74 
     4.1 Antiderivatives and Indefinite Integration (242).................................................................................... 79 
     4.2 Area (242) .............................................................................................................................................. 83 
     4.3 Riemann Sums and Definite Integrals (265) .......................................................................................... 87 
     4.4 The Fundamental Theorem of Calculus (275) ....................................................................................... 90 
     Slope Fields (Appendix pg. A6)................................................................................................................... 94 
     4.5 Integration by Substitution (288) ........................................................................................................... 97 
     4.6 Numerical Integration (300) ................................................................................................................. 100 
     5.1 The Natural Log Function: Differentiation (314) ................................................................................ 103 
     5.2 The Natural Log Function: Integration (324)....................................................................................... 106 
     5.3 Inverse Functions (332) ....................................................................................................................... 109 
     5.4 Exponential f(x)s: Differentiation & Integration (341) ........................................................................ 112 
     5.5 Bases Other than e and Applications (351) .......................................................................................... 115 
     5.6 Differential Equations: Grow and Decay (361) ................................................................................... 118 
     5.7 Differential Eqs: Separation of Variables (369) ................................................................................... 120 
     5.8 Inverse Trig Functions - Differentiation (380)..................................................................................... 123 
     5.9 Inverse Trig Functions - Integration (388) ........................................................................................... 126 
     7.7 Indeterminate Forms and L'Hopital's Rule (530) ................................................................................. 128 
     6.1 Area of Region Between Two Curves (412) ........................................................................................ 130 
     6.2 Volume the Disk Method (421) ........................................................................................................... 133 
     6.3 Volume the Shell Method (432) ........................................................................................................... 137 
                                               3 
      
              Notes #1-1                        
              Date: ______                     
                                              1.2 Finding Limits Graphically and Numerically (48)  
                                               
              Letter of recommendation:          lim f(x) = L     * The limit (L) of f(x) as x approaches c. 
              participate in class, stand      xc  
              out – in a good way!             
                                                                         2
              1) A penny: .01 =                                        x 32x
                                                             lim           x2           = ?          
              2) Go ½ the distance                         x   2
                 each time over 10 ft.   
                                                             x      1.75         1.9       1.999          2       2.001         2.1        2.25 
                                                             y            ?    
                                               
                                              Ex.1 Find                     1c osx numerically and graphically. 
                                                                    lim           x
                                                                  x   0
                                               
                                               
                                               
               
                                               
                                                                               3 x  -2
                                              Ex.2                 fx()                              ? 
                                                           lim             1 x  -2
                                                         x 2                
              “hiccup” function                
                                                           *  Existence at the 
               
                                                                point is irrelevant. 
                                               
                                               
               
                                              Limits that fail to exist: 
                                              1. f(x) approaches different values from the left and right 
                                                                                                                  f ()xf                   (x)
                                                   sides of c.                                           lim                     lim              
                                                                                                                
                                                                                                       xc  xc  
                                                                                                     from the left            from the right 
                                               
                                               
              Diving board f(x)                                                           2 x  1
                                              Ex.3  lim f ()x  if   fx()                                    
              Exists everywhere else.                    x 1                                0 x  1
                    f ()x                                                                
               lim                             
               x0
                                               
               
               limf ()x                       
               x3
                                                                                                                                                          4 
               
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...Ap calculus ab notes arbor view hs name period table of contents finding limits graphically and numerically evaluating analytically continuity one sided infinite at infinity the derivative tangent line problem basic differentiation rules day rates change product quotient trigonometric higher order derivatives chain rule implicit related extrema on an interval rolle s mean value theorems increasing decreasing f x st test concavity nd summary curve sketching optimization newton method differentials antiderivatives indefinite integration area riemann sums definite integrals fundamental theorem slope fields appendix pg a by substitution numerical natural log function inverse functions exponential bases other than e applications differential equations grow decay eqs separation variables trig indeterminate forms l hopital region between two curves volume disk shell date letter recommendation lim limit as approaches c participate in class stand xc out good way penny go distance each time over...

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