597
Index
• E •
end behavior of polynomials, 14, 158–159
equations
absolute value, 11, 142–143
finding
of normal lines, 58, 266–268
of tangent lines, 57, 265–266
of tangent lines using implicit differentiation,
61, 274–277
linear, 10, 138–139
of periodic functions, 23–26, 178–179
polynomial, 11, 141–142
quadratic, 10–11, 139–141
rational, 11, 144–145
trigonometric, 22–23, 26–27, 173–176,
182–185
estimating values with linearizations, 64,
233–234, 236–237, 279–283
evaluating
definite integrals using limits and Riemann
sums, 78
differentials, 64, 278
hyperbolic functions using definitions,
101–102, 482–483
indeterminate forms using L’Hôpital’s rule,
103–105, 489–502
limits, 31–32, 186–196
trigonometric limits, 33, 198–202
exponential functions, 55, 57, 262–265
exponents, writing using radical notation, 9, 133
• F •
factoring, 11, 141–142
finding. See also solving
angles in coordinate plane, 19–20, 168
antiderivatives
of hyperbolic functions, 102–103, 485–489
involving inverse trigonometric functions,
101, 475–481
common trigonometric values, 21, 168–170
derivatives
with chain rule, 52–54, 248–256
with fundamental theorem of calculus, 80,
354–361
of hyperbolic functions, 102, 485–489
involving exponential functions, 57, 262–265
involving inverse trigonometric functions,
100, 471–475
with power rule, 47–48, 234–236
by using definition, 45, 226–233
using implicit differentiation, 60, 268–271
using logarithmic differentiation, 56, 260–262
using product rule, 50–51, 237–242
using quotient rule, 51–52, 242–248
domain and range of a function and its inverse,
10, 137–138
domain from graphs, 13–14, 157–158
equations
of normal lines, 58, 266–268
of tangent lines, 57, 265–266
of tangent lines using implicit differentiation,
61, 274–277
graph points, 48, 236–237
intervals of increase and decrease, 68, 293–296
inverses, 9–10, 135–137
limits from graphs, 30–31, 186
linearizations, 64, 233–234, 236–237, 279–283
local maxima/minima
using first derivative test, 68, 296–300
using second derivative test, 69, 307–311
maxima from graphs, 66–67, 290–291
minima from graphs, 66–67, 290–291
partial fraction decomposition, 117–118,
557–560
range from graphs, 13–14, 157–158
speed, 70–71, 318–321
value of derivatives using graphs, 46–47,
233–234
velocity, 70–71, 318–321
volume
using cross-sectional slices, 91, 422–429
using cylindrical shells, 92–93, 429–448
volume using disks and washers, 89–91,
406–421
first derivative test, finding local maxima/
minima using, 68, 296–300
fractions, simplifying, 8, 127–131
functions
average value of, 97–98, 463–470
continuous, 40
exponential, 55, 57, 262–265
finding domain of, 10, 137–138
finding range of, 10, 137–138
graphing, 12–13, 137–138, 150–157, 222–223,
223–224, 262–265
hyperbolic
evaluating using definitions, 101–102, 482–483
finding antiderivatives of, 102–103, 485–489
Index
• E •
end behavior of polynomials, 14, 158–159
equations
absolute value, 11, 142–143
finding
of normal lines, 58, 266–268
of tangent lines, 57, 265–266
of tangent lines using implicit differentiation,
61, 274–277
linear, 10, 138–139
of periodic functions, 23–26, 178–179
polynomial, 11, 141–142
quadratic, 10–11, 139–141
rational, 11, 144–145
trigonometric, 22–23, 26–27, 173–176,
182–185
estimating values with linearizations, 64,
233–234, 236–237, 279–283
evaluating
definite integrals using limits and Riemann
sums, 78
differentials, 64, 278
hyperbolic functions using definitions,
101–102, 482–483
indeterminate forms using L’Hôpital’s rule,
103–105, 489–502
limits, 31–32, 186–196
trigonometric limits, 33, 198–202
exponential functions, 55, 57, 262–265
exponents, writing using radical notation, 9, 133
• F •
factoring, 11, 141–142
finding. See also solving
angles in coordinate plane, 19–20, 168
antiderivatives
of hyperbolic functions, 102–103, 485–489
involving inverse trigonometric functions,
101, 475–481
common trigonometric values, 21, 168–170
derivatives
with chain rule, 52–54, 248–256
with fundamental theorem of calculus, 80,
354–361
of hyperbolic functions, 102, 485–489
involving exponential functions, 57, 262–265
involving inverse trigonometric functions,
100, 471–475
with power rule, 47–48, 234–236
by using definition, 45, 226–233
using implicit differentiation, 60, 268–271
using logarithmic differentiation, 56, 260–262
using product rule, 50–51, 237–242
using quotient rule, 51–52, 242–248
domain and range of a function and its inverse,
10, 137–138
domain from graphs, 13–14, 157–158
equations
of normal lines, 58, 266–268
of tangent lines, 57, 265–266
of tangent lines using implicit differentiation,
61, 274–277
graph points, 48, 236–237
intervals of increase and decrease, 68, 293–296
inverses, 9–10, 135–137
limits from graphs, 30–31, 186
linearizations, 64, 233–234, 236–237, 279–283
local maxima/minima
using first derivative test, 68, 296–300
using second derivative test, 69, 307–311
maxima from graphs, 66–67, 290–291
minima from graphs, 66–67, 290–291
partial fraction decomposition, 117–118,
557–560
range from graphs, 13–14, 157–158
speed, 70–71, 318–321
value of derivatives using graphs, 46–47,
233–234
velocity, 70–71, 318–321
volume
using cross-sectional slices, 91, 422–429
using cylindrical shells, 92–93, 429–448
volume using disks and washers, 89–91,
406–421
first derivative test, finding local maxima/
minima using, 68, 296–300
fractions, simplifying, 8, 127–131
functions
average value of, 97–98, 463–470
continuous, 40
exponential, 55, 57, 262–265
finding domain of, 10, 137–138
finding range of, 10, 137–138
graphing, 12–13, 137–138, 150–157, 222–223,
223–224, 262–265
hyperbolic
evaluating using definitions, 101–102, 482–483
finding antiderivatives of, 102–103, 485–489