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