Page 295 - Calculus Workbook For Dummies

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Index

• F • graphs. See also functions
continuity
factoring method, 40–43 definition, 31–32
first derivative test problems, 33–36
curves, shape analysis, 269 solutions, 37–38
local extrema, 91–94, 270 of curves
rates, 269 identifying as a function, 19
sign changes, 270 review, 20–21
slopes, 269 vertical line test, 19
FOILing method, 40–43 limits
fractions definition, 31–32
difference quotient, 7 problems, 33–36
partial, 201–204 solutions, 37–38
review guess and check method, 183–184
problems, 7–8
solutions, 15–18 • H •
frowns and smiles, curve shapes, 102–105
functions. See also derivatives; graphs highest/lowest points, curves, 98–101
average value of, 219–220 high-order-derivatives rule, 80–81
compositions of, 75–77 hills and valleys, curves, 91–97
continuity horizontal asymptote, 47
definition, 31–32 hypotenuse, length calculation, 12
problems, 33–36
solutions, 37–38 • I •
definition, 19
identifying, 19 implicit differentiation rule, 78–79
length along, 227–228 improper integrals, 231–233
limits indefinite integrals, 179–182, 274
definition, 31–32 index of summation, 162
problems, 33–36 infinite limits of integration, 231–233
solutions, 37–38 infinite series
product of two, 72–74 13231 mnemonic, 267
quotient of two, 72–74 33333 mnemonic, 265–266
review absolute convergence, 253–254
problems, 20–21 alternating series, 253–254
solutions, 25–28 comparison tests, 247–250
selecting, 193–196 conditional convergence, 253–254
vertical line test, 19 definition, 243
Fundamental Theorem of Calculus, direct comparison test, 247–250
179–182, 274 geometric series, 245–246
integral comparison test, 247–250
• G • limit comparison test, 247–250
problems, 244–254
geometric series, convergence/divergence p-series, 245–246
testing, 245–246 ratio test, 251–254
geometry review root test, 251–254
problems, 12–14 sequences, 243
solutions, 15–18 solutions, 255–261
telescoping series, 245–246
testing for divergence/convergence, 245–254