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LESSON 1 The Limit of a Function...................................................... 11
LESSON 2 Calculating Limits Using the Properties of Limits....................... 17
LESSON 3 Limits at Infinity.............................................................. 23
LESSON 4 Continuity...................................................................... 30
LESSON 5 Average Rate of Change and Instantaneous Rate of Change.......... 36
LESSON 6 Derivatives..................................................................... 43
LESSON 7 Differentiation Rules......................................................... 48
LESSON 8 Differentiation Rules......................................................... 54
LESSON 9 The Chain Rule............................................................... 60
LESSON 10 Implicit Differentiation...................................................... 66
LESSON 11 Derivatives of Inverse Trig Functions and Higher Derivatives....... 72
LESSON 12 Indeterminate Forms And L¡¯Hospital¡¯s Rule.............................. 79
LESSON 13 Related Rates.................................................................. 86
LESSON 14 Linear Approximations And Differentials................................ 92
LESSON 15 Maximum And Minimum Values........................................... 99
LESSON 16 The Mean Value Theorem And Rolle¡¯s Theorem........................ 106
LESSON 17 Understanding A Curve From The First And Second Derivatives.... 111
LESSON 18 Optimization Problems...................................................... 118
LESSON 19 Indefinite Integrals........................................................... 123
LESSON 20 The Definite Integral......................................................... 129
LESSON 21 Numerical Approximations Of Integration............................... 135
LESSON 22 The Fundamental Theorem Of Calculus.................................. 141
LESSON 23 The U-Substitution Rule..................................................... 148
LESSON 24 Area Between Curves........................................................ 155
LESSON 25 Average Value Of A Function and Arc Length........................... 161
LESSON 26 Volumes Of Solids Of Revolution.......................................... 166
LESSON 27 Volumes Of Solids Of Cross-Sections..................................... 174
LESSON 28 Differential Equations....................................................... 181
LESSON 29 Logarithmic Differentiation................................................. 191
LESSON 30 Indeterminate Products and Indeterminate Powers.................... 196
LESSON 31 Derivative And Arc Length Of Parametric Equations................... 203
LESSON 32 Volumes By Cylindrical Shells.............................................. 209
LESSON 33 Integration By Parts.......................................................... 217
LESSON 34 Trigonometric Integrals...................................................... 223
LESSON 35 Integration By Partial Fractions............................................ 229
LESSON 36 Improper Integrals........................................................... 235
LESSON 37 Differential Equations....................................................... 241
LESSON 38 Derivative, Arc Length, And Area With Polar Coordinates............ 249
LESSON 39 Sequences...................................................................... 257
LESSON 40 Convergence And Divergence Of Series, Part I......................... 262
LESSON 41 Convergence And Divergence Of Series, Part II........................ 271
LESSON 42 Strategy For Testing Series.................................................. 278
LESSON 43 Power Series................................................................... 284
LESSON 44 Representations Of Functions As Power Series......................... 290
LESSON 45 Taylor And Maclaurin Series................................................ 296 |
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