Math 142

Chapter 11 Homework

section

handouts

note to yourself
of due date

homework problems
11.1
Sequences 		handout   5, 17, 19, 21, 23, 29 (hint: simplify first using algebra to get rid of the factorial (!) sign - cancellation heaven), 35, 39, 45.
11.1
Sequences 		optional problems   problems (do the circled ones)
solutions
Varberg, Purcell, Ridgon (8th ed) § 10.1
pre-11.2
Series
Series Summary
Series Flow Chart
  Before the class lecture on Section 11.2, read Section 11.2 in the textbook. This is a hard section so you will greatly benifit from reading the textbook before attending the lecture.
11.2
Series
  • geometric series
  • telescoping series
  • nth term test for divg.
 		 
  • Basics: 1, 10, 17, 19, 21, 23, 25, 29, 31, 35, 38.
    Solutions
  • Challenging but important: 65, 66, 68, 69, 70, 73a.
    Solutions
11.2
Series 		optional problems   problems
solutions
Varberg, Purcell, Ridgon (8th ed) § 10.2
Covers: geometric series, telescoping series, and nth term test for divg.
11.3
Integral Test
(positive term series) 		handout   9, 15, 19, 21, 27, 31.
11.3
Integral Test
(positive term series) 		optional problems   problems
solutions
Varberg, Purcell, Ridgon (8th ed) § 10.3
11.4
CT & LCT
(positive term series) 		handout   1, 2, 3, 5, 7, 9, 11, 13, 17, 21, 29, 31, 39, 40a, 40b (also do using the helpful intuition from class), 41a, 41b (also do (i) and explain why you cannot do (ii) using the helpful intuition from class), 43.
Sol'n
11.5
AST 		    1ab, 3, 5, 7, 9, 11, 13, 15, 17, 19.
11.6
Ratio & Root Tests 		    1, 3, 5, 7, 9, 11 (hint: e^(1/n)/n^3 <= e/n^3), 15 (hint: |arctan n| <= pi/2), 17, 21, 23, 25, 29, 33 (important for § 11.8).
11.7
Strategy for Testing Series 		   
  • Read the section. A formal lecture will not be given in class. Section 11.7 is a review of Sections 11.2 - 11.6.
  • Determine whether the series is absolutely convergent, conditionally convergent, or divergent for 1 - 37 odd (omit 29).
  • Sol'n
11.2 - 11.7
a review 		    After finishing the homework for Sections 11.1 - 11.7, do the 15 problems on the (linked) Serious Series Problems handout.
After giving these 15 Serious Series Problems a hard honest shot, look at the (linked) Answers and Hints handout.
11.4 & 11.6
CT, LCT, RT, RT 		optional problems   problems
solutions
Varberg, Purcell, Ridgon (8th ed) § 10.4
11.5
AST 		optional problems   problems
solutions
Varberg, Purcell, Ridgon (8th ed) § 10.5
11.8
Power Series 		lecture notes   Click here for your homework assignment.
Sol'n for 63.
Answers to the other 6 problems.
Exam 2
Helpful for
11.9 - 11.11 		   
11.5 revisited
Alternating Series Estimation Thm. (ASET) 		    Following the instructions in
Homework (and an example)
do 23, 25, 27, 29.
11.9
Repr. Functions as Power Series 		handout   1, 5, 7, 11, 13, 14, 15, 23
Some Solutions
pre 11.10 & 11.11
Taylor Series & Polynominals 		    Work through this
Taylor/Maclaurin Polynomial warm-up
handout before we start these sections. The homework listed at the top of the page is due at the start of the lecture!
11.10 & 11.11
Taylor Series & Polynomials 		handout
lecture notes 		  Here is a PDF file of the homework.
Give the problems a good honest shot before looking at the solutions:
11.10 & 11.11
Taylor Series & Polynomials 		handout   A nice read on Taylor Polynomials and Series from How to Ace the rest of Calculus by Adams, Hass, and Thompson

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