599
Index
intervals of increase/decrease, 68, 293–296
inverse trigonometric functions
about, 26
finding
antiderivatives using, 101, 475–481
derivatives involving, 100, 471–475
problem types, 99
tips for, 99
inverses
finding, 9–10, 135–137
solving trigonometric equations using, 26–27,
182–185
• K •
Kase, Elleyne (author)
Pre-Calculus For Dummies, 3
Kuang, Yuang (author)
Pre-Calculus For Dummies, 3
• L •
left endpoints, calculating Riemann sums with,
76, 338–340
L’Hôpital’s rule, 103–105, 489–502
limits
applying the squeeze theorem, 32–33, 196–198
classifying discontinuities, 38–40, 218–221
continuity, 39–40
discontinuities, 39–40
evaluating, 31–32, 186–196
evaluating definite integrals using, 78, 350–353
finding expressions for definite integrals with,
77, 346–348
from graphs, 30–31, 36–37, 186, 207–208
horizontal asymptotes, 38, 215–218
infinite, 33–37, 202–214
intermediate value theorem, 41, 224–225
tips for, 29
trigonometric, 33, 198–202
types of problems, 29
linear equations, 10, 138–139
linearizations, estimating values with, 63,
233–234, 236–237, 279–283
local maxima/minima, 68, 296–300, 307–311
logarithmic differentiation, finding derivatives
using, 56, 260–262
logarithmic functions, derivatives involving, 55,
56, 256–260
long division of polynomials, 15, 162–163
• M •
maxima and minima
closed interval method, 67, 291–293
first derivative test, 68, 296–300
from graphs, 66–67, 290–291
optimization problems, 71–72, 321–335
second derivative test, 69, 307–311
mean value theorem, solving problems with, 70,
313–316
midline, 23, 177
midpoints, calculating Riemann sums with, 77,
343–345
multiplying polynomials, 15, 161
• N •
net change theorem, 84–85, 375–377
Newton’s method, approximating roots using,
73, 335–338
normal lines, finding equations of, 58, 266–268
• O •
online practice, registering for, 2
optimization problems, solving, 71–72, 321–335
• P •
partial fractions
decomposition, 117–118, 557–560
integrals involving, 118–119, 561–569, 589–591
problem types, 113
tips for, 114
period, 23, 177
periodic functions, equations of, 23–26, 178–179
phase shift, 23, 177
polynomial equations, solving by factoring, 11,
141–142
polynomial inequalities, 12, 145–149
polynomials
adding, 14, 159
end behavior of, 14, 158–159
long division of, 15, 162–163
multiplying, 15, 161
subtracting, 14–15, 160
position, relating with velocity, 70, 316–318
power rule, finding derivatives with, 47–48,
234–236
Index
intervals of increase/decrease, 68, 293–296
inverse trigonometric functions
about, 26
finding
antiderivatives using, 101, 475–481
derivatives involving, 100, 471–475
problem types, 99
tips for, 99
inverses
finding, 9–10, 135–137
solving trigonometric equations using, 26–27,
182–185
• K •
Kase, Elleyne (author)
Pre-Calculus For Dummies, 3
Kuang, Yuang (author)
Pre-Calculus For Dummies, 3
• L •
left endpoints, calculating Riemann sums with,
76, 338–340
L’Hôpital’s rule, 103–105, 489–502
limits
applying the squeeze theorem, 32–33, 196–198
classifying discontinuities, 38–40, 218–221
continuity, 39–40
discontinuities, 39–40
evaluating, 31–32, 186–196
evaluating definite integrals using, 78, 350–353
finding expressions for definite integrals with,
77, 346–348
from graphs, 30–31, 36–37, 186, 207–208
horizontal asymptotes, 38, 215–218
infinite, 33–37, 202–214
intermediate value theorem, 41, 224–225
tips for, 29
trigonometric, 33, 198–202
types of problems, 29
linear equations, 10, 138–139
linearizations, estimating values with, 63,
233–234, 236–237, 279–283
local maxima/minima, 68, 296–300, 307–311
logarithmic differentiation, finding derivatives
using, 56, 260–262
logarithmic functions, derivatives involving, 55,
56, 256–260
long division of polynomials, 15, 162–163
• M •
maxima and minima
closed interval method, 67, 291–293
first derivative test, 68, 296–300
from graphs, 66–67, 290–291
optimization problems, 71–72, 321–335
second derivative test, 69, 307–311
mean value theorem, solving problems with, 70,
313–316
midline, 23, 177
midpoints, calculating Riemann sums with, 77,
343–345
multiplying polynomials, 15, 161
• N •
net change theorem, 84–85, 375–377
Newton’s method, approximating roots using,
73, 335–338
normal lines, finding equations of, 58, 266–268
• O •
online practice, registering for, 2
optimization problems, solving, 71–72, 321–335
• P •
partial fractions
decomposition, 117–118, 557–560
integrals involving, 118–119, 561–569, 589–591
problem types, 113
tips for, 114
period, 23, 177
periodic functions, equations of, 23–26, 178–179
phase shift, 23, 177
polynomial equations, solving by factoring, 11,
141–142
polynomial inequalities, 12, 145–149
polynomials
adding, 14, 159
end behavior of, 14, 158–159
long division of, 15, 162–163
multiplying, 15, 161
subtracting, 14–15, 160
position, relating with velocity, 70, 316–318
power rule, finding derivatives with, 47–48,
234–236