534
INDEX
first order, 394
solution, 392
disk method, 346
distance traveled, 212
diverge
sequence, 451
Divergence Test, 474
domain, 130
equilibrium solution, 404
stable, 404
unstable, 405
error, 323
error functin, 281
error function, 316
Euler’s Method, 410
error, 415
extreme value, 162
extreme value theorem, 184
Fibonacci sequence, 447
first derivative test, 164
foot-pound, 366
forward difference, 46
FTC, 254
function, 130
function-derivative pair, 292
Fundamental Theorem of Calculus
First, 276
Second, 278
fundamental theorem of calculus, 252
geometric series, 458
common ratio, 459
geometric sum, 457
harmonic series, 474
Hooke’s Law, 368
implicit function, 142
improper integral, 378
converges, 380
diverges, 380
unbounded integrand, 381
unbounded region of integration, 379
increasing, 53
indefinite integral, 291
evaluate, 291
indeterminate, 15
infinite series, 470
infinity, 154
inflection point, 169
initial condition, 270
instantaneous rate of change, 24, 44
instantaneous velocity, 4, 17
integral function, 271
integral sign, 237
integral test, 474, 477
integrand, 237
integration by parts, 301
interval of convergence, 508
L’Hopital’s rule, 151, 157
Lagrange error bound, 513
left limit, 66
lemniscate, 141
limit
definition, 13
one-sided, 66
limit comparison test, 478
limits of integration, 237
local linearization, 79
locally linear, 72
logistic, 439
logistic equation, 439
solution, 442
Maclaurin series, 507
mass, 355
maximum
absolute, 162
global, 162
local, 162
relative, 162
midpoint rule
error, 323
minimum
INDEX
first order, 394
solution, 392
disk method, 346
distance traveled, 212
diverge
sequence, 451
Divergence Test, 474
domain, 130
equilibrium solution, 404
stable, 404
unstable, 405
error, 323
error functin, 281
error function, 316
Euler’s Method, 410
error, 415
extreme value, 162
extreme value theorem, 184
Fibonacci sequence, 447
first derivative test, 164
foot-pound, 366
forward difference, 46
FTC, 254
function, 130
function-derivative pair, 292
Fundamental Theorem of Calculus
First, 276
Second, 278
fundamental theorem of calculus, 252
geometric series, 458
common ratio, 459
geometric sum, 457
harmonic series, 474
Hooke’s Law, 368
implicit function, 142
improper integral, 378
converges, 380
diverges, 380
unbounded integrand, 381
unbounded region of integration, 379
increasing, 53
indefinite integral, 291
evaluate, 291
indeterminate, 15
infinite series, 470
infinity, 154
inflection point, 169
initial condition, 270
instantaneous rate of change, 24, 44
instantaneous velocity, 4, 17
integral function, 271
integral sign, 237
integral test, 474, 477
integrand, 237
integration by parts, 301
interval of convergence, 508
L’Hopital’s rule, 151, 157
Lagrange error bound, 513
left limit, 66
lemniscate, 141
limit
definition, 13
one-sided, 66
limit comparison test, 478
limits of integration, 237
local linearization, 79
locally linear, 72
logistic, 439
logistic equation, 439
solution, 442
Maclaurin series, 507
mass, 355
maximum
absolute, 162
global, 162
local, 162
relative, 162
midpoint rule
error, 323
minimum