next up previous
Next: About this document

Exercise Set 21, p. 163

  1. tex2html_wrap_inline273
  2. x
  3. tex2html_wrap_inline277
  4. tex2html_wrap_inline279
  5. 0
  6. The graph looks like Figure 67 on P. 158. tex2html_wrap_inline283
  7. The graph looks like Figure 68 on P. 158. tex2html_wrap_inline285
  8. tex2html_wrap_inline287
  9. tex2html_wrap_inline289
  10. tex2html_wrap_inline291
  11. tex2html_wrap_inline293
  12. tex2html_wrap_inline295
  13. tex2html_wrap_inline297
  14. tex2html_wrap_inline299
  15. tex2html_wrap_inline301
  16. tex2html_wrap_inline303
  17. tex2html_wrap_inline305
  18. tex2html_wrap_inline307
  19. tex2html_wrap_inline309
  20. tex2html_wrap_inline311
  21. 2
  22. tex2html_wrap_inline315

Exercise Set 22, p. 169

  1. tex2html_wrap_inline317 , tex2html_wrap_inline319 , tex2html_wrap_inline321 , tex2html_wrap_inline323 , tex2html_wrap_inline325 , tex2html_wrap_inline327 , tex2html_wrap_inline329 , tex2html_wrap_inline331 , tex2html_wrap_inline333 , tex2html_wrap_inline335 ,
  2. tex2html_wrap_inline337
  3. Let tex2html_wrap_inline339 , so that tex2html_wrap_inline341 and as tex2html_wrap_inline343 we get tex2html_wrap_inline345 , then

Exercise Set 23, p. 178

  1. tex2html_wrap_inline347
  2. tex2html_wrap_inline349
  3. tex2html_wrap_inline351 .
  4. tex2html_wrap_inline353 .
  5. tex2html_wrap_inline355 .
  6. tex2html_wrap_inline357 .
  7. tex2html_wrap_inline359 .

Exercise Set 24, p. 181

  1. tex2html_wrap_inline361 and tex2html_wrap_inline363 . Clearly n+3>n+2 and so tex2html_wrap_inline367 is increasing and .
  2. tex2html_wrap_inline371 and tex2html_wrap_inline373 . Consider tex2html_wrap_inline375 :

    Therefore tex2html_wrap_inline377 and the series increases. .

  3. tex2html_wrap_inline381 and tex2html_wrap_inline383

    Therefore tex2html_wrap_inline377 and the series increases. .

  4. tex2html_wrap_inline389 and tex2html_wrap_inline391 .

    Thus tex2html_wrap_inline367 is increasing and .

  5. tex2html_wrap_inline397 and tex2html_wrap_inline399 .

    So tex2html_wrap_inline367 is increasing and .

  6. For n from 1 to 15, tex2html_wrap_inline411 runs like 0, 0.70711, 0.81650, 0.86603, 0.89443, 0.91287, 0.92582, 0.93541, 0.94281, 0.94868, 0.95346, 0.95743, 0.96077, 0.96362, 0.96609. You can tell that the limit must be 1. For the graph, see Figure 72 on P. 167.
  7. tex2html_wrap_inline445
  8. Apply the box method to Fact # 5:

    Now let tex2html_wrap_inline447 . Note that tex2html_wrap_inline449 as tex2html_wrap_inline345 and we are done.

  9. Use n=4 in the expression tex2html_wrap_inline455 to get tex2html_wrap_inline457 .
  10. The graph of tex2html_wrap_inline459 has the same shape as the graph of tex2html_wrap_inline461 except for two minor differences: first, it is steeper, and second, it `shoots' through (1,1) instead of (0,1).
  11. a)
    1
    b)
    0
    c)
    5
    d)
    1
    e)
    0
    f)
    0
    g)
    tex2html_wrap_inline479
    h)
    tex2html_wrap_inline481
    i)
    x-1
    j)
    0
  12. 0
  13. a)
    tex2html_wrap_inline489 .
    b)
    tex2html_wrap_inline491 .
    c)
    tex2html_wrap_inline493 .
    d)
    tex2html_wrap_inline495 .
    e)
    tex2html_wrap_inline497 .

  14. tex2html_wrap_inline499 .
  15. a)
    tex2html_wrap_inline501 .
    b)
    tex2html_wrap_inline503 .
    c)
    tex2html_wrap_inline505 .
    d)
    tex2html_wrap_inline507 .
    e)
    1.
    f)
    tex2html_wrap_inline511 .
    g)
    tex2html_wrap_inline513 .
    h)
    tex2html_wrap_inline515 .
    i)
    tex2html_wrap_inline517 .
    j)
    tex2html_wrap_inline519 .
    k)
    tex2html_wrap_inline521 .

Exercise Set 25, p. 186

  1. a)
    tex2html_wrap_inline523 .
    b)
    tex2html_wrap_inline525 .
    c)
    tex2html_wrap_inline527 .
    d)
    tex2html_wrap_inline529
    e)
    tex2html_wrap_inline531 .
    f)
    tex2html_wrap_inline533 .
    g)
    tex2html_wrap_inline535 .
    h)
    tex2html_wrap_inline537 .
    i)
    tex2html_wrap_inline539 .
    j)
    tex2html_wrap_inline541 .

Chapter Exercises, p. 192

  1. tex2html_wrap_inline543 and tex2html_wrap_inline545 . Clearly n+4>n+2 and so tex2html_wrap_inline367 is increasing and .
  2. tex2html_wrap_inline553 and tex2html_wrap_inline555 .

    Therefore tex2html_wrap_inline377 and the series increases. .

  3. tex2html_wrap_inline561 and tex2html_wrap_inline563

    Therefore tex2html_wrap_inline377 and the series increases. .

  4. tex2html_wrap_inline569 and tex2html_wrap_inline571 .

    Thus tex2html_wrap_inline367 is increasing and .

  5. Use tex2html_wrap_inline577
  6. a)
    tex2html_wrap_inline579
    b)
    tex2html_wrap_inline581
  7. a)
    tex2html_wrap_inline583
    b)
    tex2html_wrap_inline585
    c)
    tex2html_wrap_inline587
  8. a)
    tex2html_wrap_inline589
    b)
    tex2html_wrap_inline591
    c)
    tex2html_wrap_inline593
    d)
    tex2html_wrap_inline595
    e)
    0
    f)
    tex2html_wrap_inline599
    g)
    1
    h)
    tex2html_wrap_inline603
    i)
    tex2html_wrap_inline605 .
    j)
    2.
    k)
    tex2html_wrap_inline609 .
    l)
    tex2html_wrap_inline611
    m)
    tex2html_wrap_inline613

next up previous
Next: About this document

Angelo Mingarelli
Mon Nov 2 10:55:54 EST 1998