Homework Assignment for M 408D -- Shirley

M 408D Spring 2024 Homework # 3

The Homework #3 solutions will be turned in at the beginning of class in a stapled, fully documented packet, folded along the center vertical line.

Part I: Section 7.8:

  • # 13, 19, 29, 36, 42, 48

Part II: Section 11.1:

  • # 6, 18, 31, 34, 36, 44, 47, 55,

Part III: Complete the SOPS Worksheet:

  • To view or download the SOPS Worksheet: ==> Click Here.

  • You don't need to hand in the worksheet, just the write the 5 values for each exercise on your own paper.

  • Also, it is obvious that you could copy your answers from the worksheet, but you will get more value from these exercises if you actually add the sums up by hand or use your calculator to calculate the terms in the sequence of partial sums (SOPS).

Part IV: Section 11.2:

  • # 28, 29, 30, 32, 38, 45, 60, 61

    • It is important that you read and understand "Theorem 6" and "Note 1" on page 745.

    • It is also important that you read and understand the Note after "Example 9" on page 746.

    • Whenever you conclude that a GEOMETRIC SERIES is convergent or divergent, you are required to write out a full sentence giving a clear and complete justification of your conclusion. To see a suggested (even recommended) wording of this justification:==> Click Here.

    • Whenever you conclude that a series is divergent by the Test for Divergence, you are required to write out a full sentence giving a clear and complete justification of your conclusion. To see a suggested (even recommended) wording of this justification:==> Click Here.

Part V: Section 11.3:

  • # 5, 6, 17, 18, 19

    • Whenever you read the phrase "Estimate the error", replace this with the phrase "Estimate the LEVEL OF error."

    • Read the handout "Correct to Three Decimal Places???" in the "Reference Pages" Handouts folder.
    • Whenever you conclude that a series is convergent or divergent by the Integral Test, you are required to write out full sentences giving a clear and complete justification of your conclusions. To see a suggested (even recommended) wording of these justifications:==> Click Here.

    • Whenever you conclude that a p-series is convergent or divergent because you are applying Theorem 1 on page 754, you are required to write out a full sentence giving a clear and complete justification of your conclusion. To see a suggested (even recommended) wording of this justification:==> Click Here.

    • See the handout "Model Solutions for P-Test problems and the Integtral Test problems." in the "Sequences and Series" folder.

    • See the "TABLE 01 of Useful Calculations."

      • To view or download this table:==> Click Here.

      • If you use any table of calculations like these, verify the first three lines of that table with your calculator.

    • To see a table showing an infinite limit of arctan(x):==> Click Here.