596 1,001 Calculus Practice Problems For Dummies
continuous functions, 40
convergent improper integrals, 122–123,
573–589
coordinate plane, finding angles in, 19–20, 168
cross-sectional slices, finding volume using, 91,
422–429
cylindrical shells, finding volume using, 92–93,
429–448
• D •
decomposition, partial fraction,
117–118, 557–560
definite integrals. See also applications of
derivatives
determining differentiability
from graphs, 44, 226
evaluating using limits and Riemann sums, 78,
350–353
examples of, 80–81, 361–365
finding
area between curves, 88–89, 387–406
average value of functions, 97–98, 463–470
expressions of definite integrals using limits
and Riemann sums, 77, 346–348
with fundamental theorem of calculus, 80,
354–361
graph points, 48, 236–237
of hyperbolic functions, 102, 485–489
involving exponential functions, 57, 262–265
involving inverse trigonometric functions,
100, 471–475
from limit and Riemann sum form, 78,
348–350
with power rule, 47–48, 234–236
using chain rule, 52–54, 248–256
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
value of definite integrals using graphs,
46–47, 233–234
volume using cross-sectional slices, 91,
422–429
volume using cylindrical shells, 92–93,
429–448
volumes using disks and washers, 89–91,
406–421
involving logarithmic functions, 56, 256–260
problem types, 43, 87
tips for, 43, 87
work, 94–97
definitions, evaluating hyperbolic functions
using, 101–102, 482–483
degree measure, 18–19, 166–167
derivatives. See also applications of derivatives
determining differentiability from graphs,
44, 226
evaluating using limits and Riemann sums, 78,
350–353
examples of, 80–81, 361–365
finding
area between curves, 88–89, 387–406
average value of functions, 97–98, 463–470
expressions of derivatives using limits and
Riemann sums, 77, 346–348
with fundamental theorem of calculus, 80,
354–361
graph points, 48, 236–237
of hyperbolic functions, 102, 485–489
involving exponential functions, 57, 262–265
involving inverse trigonometric functions,
100, 471–475
from limit and Riemann sum form, 78,
348–350
with power rule, 47–48, 234–236
using chain rule, 52–54, 248–256
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
value of using graphs, 46–47, 233–234
volume using cross-sectional slices, 91,
422–429
volume using cylindrical shells, 92–93,
429–448
volumes using disks and washers, 89–91,
406–421
involving logarithmic functions, 56, 256–260
problem types, 43, 87
tips for, 43, 87
work, 94–97
differentiability determining from graphs,
44, 226
differentials, evaluating, 64, 278
discontinuities, classifying, 38–40, 218–221
displacement, 85–86, 377–379, 382–383
distance traveled, finding for particles, 85–86,
379–381, 384–386
divergent improper integrals, 122–123, 573–589
domain
finding from graphs, 13–14, 157–158
of a function and its inverse, 10, 137–138
Dummies (website), 3
continuous functions, 40
convergent improper integrals, 122–123,
573–589
coordinate plane, finding angles in, 19–20, 168
cross-sectional slices, finding volume using, 91,
422–429
cylindrical shells, finding volume using, 92–93,
429–448
• D •
decomposition, partial fraction,
117–118, 557–560
definite integrals. See also applications of
derivatives
determining differentiability
from graphs, 44, 226
evaluating using limits and Riemann sums, 78,
350–353
examples of, 80–81, 361–365
finding
area between curves, 88–89, 387–406
average value of functions, 97–98, 463–470
expressions of definite integrals using limits
and Riemann sums, 77, 346–348
with fundamental theorem of calculus, 80,
354–361
graph points, 48, 236–237
of hyperbolic functions, 102, 485–489
involving exponential functions, 57, 262–265
involving inverse trigonometric functions,
100, 471–475
from limit and Riemann sum form, 78,
348–350
with power rule, 47–48, 234–236
using chain rule, 52–54, 248–256
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
value of definite integrals using graphs,
46–47, 233–234
volume using cross-sectional slices, 91,
422–429
volume using cylindrical shells, 92–93,
429–448
volumes using disks and washers, 89–91,
406–421
involving logarithmic functions, 56, 256–260
problem types, 43, 87
tips for, 43, 87
work, 94–97
definitions, evaluating hyperbolic functions
using, 101–102, 482–483
degree measure, 18–19, 166–167
derivatives. See also applications of derivatives
determining differentiability from graphs,
44, 226
evaluating using limits and Riemann sums, 78,
350–353
examples of, 80–81, 361–365
finding
area between curves, 88–89, 387–406
average value of functions, 97–98, 463–470
expressions of derivatives using limits and
Riemann sums, 77, 346–348
with fundamental theorem of calculus, 80,
354–361
graph points, 48, 236–237
of hyperbolic functions, 102, 485–489
involving exponential functions, 57, 262–265
involving inverse trigonometric functions,
100, 471–475
from limit and Riemann sum form, 78,
348–350
with power rule, 47–48, 234–236
using chain rule, 52–54, 248–256
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
value of using graphs, 46–47, 233–234
volume using cross-sectional slices, 91,
422–429
volume using cylindrical shells, 92–93,
429–448
volumes using disks and washers, 89–91,
406–421
involving logarithmic functions, 56, 256–260
problem types, 43, 87
tips for, 43, 87
work, 94–97
differentiability determining from graphs,
44, 226
differentials, evaluating, 64, 278
discontinuities, classifying, 38–40, 218–221
displacement, 85–86, 377–379, 382–383
distance traveled, finding for particles, 85–86,
379–381, 384–386
divergent improper integrals, 122–123, 573–589
domain
finding from graphs, 13–14, 157–158
of a function and its inverse, 10, 137–138
Dummies (website), 3