Homework Assignment for M 408D -- Shirley

Homework Assignment for M 408D -- Shirley

M 408D Spring 2024 Homework # 5

The Homework #5 solutions will be turned in at the beginning of class in a stapled, fully documented packet, folded along the center vertical line.

Part ZERO: Section 11.4:

# 10, 25, 26

Whenever you conclude that a series is convergent or divergent using the Limit Comparison Test, 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. and read pages 1 and 3.

In solving the problems in Part ZERO, you MUST USE the Limit Comparison Test.

Part I: Section 11.5:

# 24, 27,30, 38, 42, 43

Whenever you conclude that an alternating series is convergent using the Alternating Series Test, 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.

It will help to read the handout The Level-of-Error Formula for a Convergent Alternating Series in the Sequences and Series handouts folder.

Recall the meaning of the term "Correct to Three Decimal Places" that we are using in this class. This meaning of this phrase is defined in the handout Correct to Three Decimal Places?

Part II: Section 11.6 : # 5, 6, 9, 39 (b and d only)

In solving these problems from section 11.6, you may not use the Root Test. Use the Ratio Test when possible.

On #5, use the Ratio Test.

Use the handouts "Algebra Review" and "Important Limits" in the Reference Pages Handouts folder when working with the Ratio Test.

Whenever you conclude that a series is convergent or divergent using the Ratio Test, 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 and read page 1.

Part III: Section 11.6 : # 5 (Again: see Note below.) , 21, 22

This time on #5, use the Root Test. It was assigned in Part II to use the Ratio Test, but both tests can be applied to this series.

In solving these problems from section 11.6, you must use the Root Test if possible.

Whenever you conclude that a series is convergent or divergent using the Root Test, 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 and read page 2.

Use the handouts "Algebra Review" and "Important Limits" in the Reference Pages Handouts folder when working with the Root Test.

Part IV: Section 11.8 : # 4, 11, 14, 20, 22, 26, 33

Use the root test in solving problem #14.

Remember, when working with power series, always to check for convergence or divergence at the endpoints of the interval of covergence individually. This endpoint check is not required for PSRs however.

Also, when concluding that, at an endpoint of the interval of convergence, the resulting series is Convergent (or Divergent), you don't need to write a full sentence justification of the conclusion -- you only need to cite which Convergence Test or Divergence Test applies to make that conclusion about that particular series (occurring at the endpoint).

It will help to read the handout First Notes on Power Series in the Power Series handouts folder.