598 1,001 Calculus Practice Problems For Dummies
finding derivatives of, 102, 485–489
problem types, 99
tips for, 99
inverse trigonometric
about, 26
finding antiderivatives using, 101, 475–481
finding derivatives involving, 100, 471–475
problem types, 99
tips for, 99
logarithmic, 55, 56, 256–260
making continuous, 40
periodic, 23–26, 178–179
fundamental theorem of calculus
definite integrals, 80–81, 361–365
displacement of particles, 85–86, 377–379,
382–386
distance traveled by particles, 85–86,
377–379, 382–386
finding derivatives with, 80, 354–361
indefinite integrals, 81–84, 365–375
problem types, 79
tips for, 79
• G •
graphs and graphing
common functions, 12–13, 150–157
determining differentiality from, 44, 226
finding
domain from, 13–14, 157–158
limits from, 30–31, 186
maxima and minima from, 66–67, 290–291
points, 48, 236–237
range from, 13–14, 157–158
value of derivatives using graphs, 46–47,
233–234
limits from, 36–37, 207–208
• H •
horizontal asymptotes, 38, 215–218
horizontal line test, 9, 133–134
hyperbolic functions
antiderivatives of, 102–103, 485–489
derivatives of, 102, 485–489
evaluating using definitions, 101–102, 482–483
problem types, 99
tips for, 99
• I •
identifying inflection points, 69, 303–307
implicit differentiation
finding derivatives using, 60, 268–271
finding equations of tangent lines using, 61,
274–277
problem types, 59
tips for, 59
improper integrals
comparison test, 123, 589–591
convergent, 122–123, 573–589
defined, 121
divergent, 122–123, 573–589
problem types, 121
Simpson’s rule, 124, 592–593
tips for, 121
trapezoid rule, 124, 591–592
indefinite integrals. See also Riemann sums
examples of, 81–84, 365–375
of hyperbolic functions, 102–103, 485–489
involving inverse trigonometric functions, 101,
475–481
indeterminate forms, evaluating using
L’Hôpital’s Rule, 103–105, 489–502
inequalities
absolute value, 12, 150
polynomial, 12, 145–149
rational, 12, 145–149
infinite limits, 33–37, 202–214
inflection points, identifying, 69, 303–307
integrals. See also definite integrals; indefinite
integrals
convergent improper, 122–123, 573–589
divergent improper, 122–123, 573–589
improper
comparison test, 123, 589–591
convergent, 122–123, 573–589
defined, 121
divergent, 122–123, 573–589
problem types, 121
Simpson’s rule, 124, 592–593
tips for, 121
trapezoid rule, 124, 591–592
involving partial fractions, 118–119, 561–569,
589–591
trigonometric, 113, 114–116, 524–537
integration, 107, 109–111, 512–524. See also
u-substitution
intermediate value theorem, 41, 224–225
functions (continued)
finding derivatives of, 102, 485–489
problem types, 99
tips for, 99
inverse trigonometric
about, 26
finding antiderivatives using, 101, 475–481
finding derivatives involving, 100, 471–475
problem types, 99
tips for, 99
logarithmic, 55, 56, 256–260
making continuous, 40
periodic, 23–26, 178–179
fundamental theorem of calculus
definite integrals, 80–81, 361–365
displacement of particles, 85–86, 377–379,
382–386
distance traveled by particles, 85–86,
377–379, 382–386
finding derivatives with, 80, 354–361
indefinite integrals, 81–84, 365–375
problem types, 79
tips for, 79
• G •
graphs and graphing
common functions, 12–13, 150–157
determining differentiality from, 44, 226
finding
domain from, 13–14, 157–158
limits from, 30–31, 186
maxima and minima from, 66–67, 290–291
points, 48, 236–237
range from, 13–14, 157–158
value of derivatives using graphs, 46–47,
233–234
limits from, 36–37, 207–208
• H •
horizontal asymptotes, 38, 215–218
horizontal line test, 9, 133–134
hyperbolic functions
antiderivatives of, 102–103, 485–489
derivatives of, 102, 485–489
evaluating using definitions, 101–102, 482–483
problem types, 99
tips for, 99
• I •
identifying inflection points, 69, 303–307
implicit differentiation
finding derivatives using, 60, 268–271
finding equations of tangent lines using, 61,
274–277
problem types, 59
tips for, 59
improper integrals
comparison test, 123, 589–591
convergent, 122–123, 573–589
defined, 121
divergent, 122–123, 573–589
problem types, 121
Simpson’s rule, 124, 592–593
tips for, 121
trapezoid rule, 124, 591–592
indefinite integrals. See also Riemann sums
examples of, 81–84, 365–375
of hyperbolic functions, 102–103, 485–489
involving inverse trigonometric functions, 101,
475–481
indeterminate forms, evaluating using
L’Hôpital’s Rule, 103–105, 489–502
inequalities
absolute value, 12, 150
polynomial, 12, 145–149
rational, 12, 145–149
infinite limits, 33–37, 202–214
inflection points, identifying, 69, 303–307
integrals. See also definite integrals; indefinite
integrals
convergent improper, 122–123, 573–589
divergent improper, 122–123, 573–589
improper
comparison test, 123, 589–591
convergent, 122–123, 573–589
defined, 121
divergent, 122–123, 573–589
problem types, 121
Simpson’s rule, 124, 592–593
tips for, 121
trapezoid rule, 124, 591–592
involving partial fractions, 118–119, 561–569,
589–591
trigonometric, 113, 114–116, 524–537
integration, 107, 109–111, 512–524. See also
u-substitution
intermediate value theorem, 41, 224–225
functions (continued)