Page 297 - Calculus Workbook For Dummies

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Index

problems, 33–36 • R •
solutions, 37–38
linear approximation, 138–139, 271 radian/degree conversions, 23
lines, 134–137 rates. See also derivatives
local extrema, 91–97, 270 calculating average, 105–107
long sums, shorthand for, 162–166 first derivative test, 269
lowest/highest points, curves, 98–101 related, 127–130
ratio test, 251–254
• M • rational functions, 47
rectangles, area under a curve, 159–161,
Mean Value Theorem, 106–107 274–275
meat slicer method, 222–226 Reimann sums, 162–166
midpoint rule, 273 related rates, 127–130
mnemonics reverse differentiation. See antiderivatives
13231, 267 right triangles, 198–201
33333, 265–266 root test, 251–254
continuity, 265–267 rules
derivatives of trigonometry functions, 271 for derivatives
infinite series, 265–267 chain, 75–77. See also implicit differentiation
limits, 265–267 derivative of a constant, 69
PSST, 271 high order derivatives, 80–81
implicit differentiation, 78–79. See also chain
• N • rule
power, 69
negative area, 177–179, 275 problems, 70–81
negative displacement, 131–134 product, 72–74
negative velocity, 131–134 quotient, 72–74, 270–271
normals, 134–137
solutions, 82–89
• O • for differentiation
chain, 75–77. See also implicit differentiation
derivative of a constant, 69
13231 mnemonic, 267 high order derivatives, 80–81
optimization, 124–126
implicit differentiation, 78–79. See also chain
rule
• P • power, 69
problems, 70–81
parallelogram, area calculation, 13
partial fractions, 201–204 product, 72–74
position, 131–134 quotient, 72–74
power rule, 69 solutions, 82–89
product rule, 72–74, 270. See also integration, L’Hôpital’s, 229–231
by parts Simpson’s, 168–170, 273–274
p-series, convergence/divergence testing, Trapezoid, 168–170, 273
245–246
PSST mnemonic, 271 • S •
Pythagorean Theorem, 198–201
sandwich method, 46–47
• Q • second derivative test
concavity, 102, 270
inflection points, 102, 270
quotient rule, 72–74, 270–271
local extrema, 95–97