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| 9.10 || Exercises || 371
| 9.10 || Exercises || 371
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! colspan="3" | PART IV: MISCELLANEOUS
! colspan="3" | 10. SEQUENCES, INFINITE SERIES, IMPROPER INTEGRALS
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! colspan="3" | Chapter 13: Functions
| 10.1 || Zeno's paradox || 374
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| 1 || Definition of a function || 313
| 10.2 || Sequences || 378
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| 2 || Polynomial functions || 318
| 10.3 || Monotonic sequences of real numbers || 381
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| 3 || Graphs of functions || 330
| 10.4 || Exercises || 382
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| 4 || Exponential function || 333
| 10.5 || Infinite series || 383
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| 5 || Logarithms || 338
| 10.6 || The linearity property of convergent series || 385
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| 10.7 || Telescoping series || 386
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| 10.8 || The geometric series || 388
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| 10.9 || Exercises || 391
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| 10.10 || Exercises on decimal expansions || 393
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| 10.11 || Tests for convergence || 394
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| 10.12 || Comparison tests for series of nonnegative terms || 394
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| 10.13 || The integral test || 397
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| 10.14 || Exercises || 398
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| 10.15 || The root test and the ratio test for series of nonnegative terms || 399
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| 10.16 || Exercises || 402
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| 10.17 || Alternating series || 403
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| 10.18 || Conditional and absolute convergence || 406
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| 10.19 || The convergence tests of Dirichlet and Abel || 407
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| 10.20 || Exercises || 409
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| 10.21 || Rearrangements of series || 411
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| 10.22 || Miscellaneous review exercises || 414
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| 10.23 || Improper integrals || 416
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| 10.24 || Exercises || 420
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! colspan="3" | 11. SEQUENCES AND SERIES OF FUNCTIONS
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| 11.1 || Pointwise convergence of sequences of functions || 422
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| 11.2 || Uniform convergence of sequences of functions || 423
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| 11.3 || Uniform convergence and continuity || 424
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| 11.4 || Uniform convergence and integration || 425
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| 11.5 || A sufficient condition for uniform convergence || 427
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| 11.6 || Power series. Circle of convergence || 428
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| 11.7 || Exercises || 430
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| 11.8 || Properties of functions represented by real power series || 431
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| 11.9 || The Taylor's series generated by a function || 434
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| 11.10 || A sufficient condition for convergence of a Taylor's series || 435
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| 11.11 || Power-series expansions for the exponential and trigonometric functions || 435
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| 11.12 || Bernstein's theorem || 437
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| 11.13 || Exercises || 438
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| 11.14 || Power series and differential equations || 439
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| 11.15 || The binomial series || 441
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| 11.16 || Exercises || 443
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! colspan="3" | Chapter 14: Mappings
! colspan="3" | Chapter 14: Mappings
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