Page 293 - Calculus Workbook For Dummies

Index

Numbers conditional convergence, 253–254
conjugate multiplication method, 40–43
13231 mnemonic, 267 constants, derivatives of, 69
33333 mnemonic, 265–266 continuity
13231 mnemonic, 267
• A • 33333 mnemonic, 265–266
definition, 31–32
absolute convergence, 253–254 problems, 33–36
absolute extrema, 98–101 solutions, 37–38
acceleration, 131–134 convergence/divergence, testing for, 245–254
algebra curves. See also derivatives; difference
review quotient
problems, 9–11 approximating area under, 159–161, 168–170
solutions, 15–18 definite integral, 166–167
solving limit problems, 39–43 exact areas, 166
alternating series, 253–254 graphs of
antiderivatives. See also integration identifying as a function, 19
area function, 177–179 review, 20–21
definition, 179 vertical line test, 19
finding, 183–187 index of summation, 162
Fundamental Theorem of Calculus, integrands, 166
179–182, 274 irregular shapes, 159–161
guess and check method, 183–184 long sums, shorthand for, 162–166
negative area, 177–179, 275 problems, 160–170
problems, 178–187 rectangles, 159–161
solutions, 188–191 Reimann sums, 162–166
substitution method, 185–187 shape analysis
approximating absolute extrema, 98–101
area under curves, 159–161, 168–170 concavity, 102–105
linear approximation, 138–139, 271 first derivative test, 91–94, 269
arc length, 227–228 highest/lowest points, 98–101
area, calculating. See integration hills and valleys, 91–97
area function, 177–179 inflections points, 102–105
average velocity, 132–134 local extrema, 91–97
Mean Value Theorem, 105–107
• C • problems, 92–107
rate, calculating average, 105–107
calculator, solving limit problems, 44–45 second derivative test, 95–97, 102
Calculus For Dummies, 61 slope, calculating average, 105–107
canceling method, 40–43 smiles and frowns, 102–105
chain rule, 75–77 solutions, 108–121
change, calculating speed of. See derivatives sigma notation, 162–166
chunking integration areas, 275 Simpson’s rule, 168–170
comparison tests, 247–250 solutions, 171–176
concavity Trapezoid rule, 168–170
curves, 102–105 cylindrical shell method, 222–226
second derivative test, 270