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MATH 152 - D100 ASSIGNMENT #7

Quiz: Friday, October 31, 2014, in-class

Instructions

Complete this assignment by Wednesday evening in your homework journal. This will give you plenty of timeto make sure you understand the material before the quiz at the end of Fridays class. Quiz questions will betaken from items 2 or 3 below.

1. Online Questions: (from LONCAPA: https://loncapa.sfu.ca):Questions in folders: 11.1, 11.2

2. Questions from textbook:

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tSt. 11.1

15 RE28 RE31 RE37 RE49 RE56 RE64 CE work out some terms, see what happens76 CE82 CE

St. 11.2

19 RE geometric series23 RE geometric series29 RE converge or diverge?31 RE converge or diverge?42 RE converge or diverge?45 CE telescoping sum47 CE telescoping sum53 RE decimal to ratio59 CE

St. 11.3

5 RE converge or diverge?12 RE converge or diverge?19 RE converge or diverge?20 RE converge or diverge?24 RE converge or diverge?37 CE approximating a sum

1See the legend on last page of this assignment for what these acronyms mean.

DR. J. MULHOLLAND, FALL 2014 1


3. Additional questions:

A1. Let the sequence {an} be defined recursively as follows:

a1 = 2, an+1 =1

2(an + 4), for n 1.

(a) Take as a fact that an < 4 for all n. (Find the first five terms of the sequence to convince yourselfthat this is true.)

(b) Prove that {an} is an increasing sequence. Conclude that {an} is a convergent sequence.(c) Find the limit of this sequence.

done checked corrected study MT study final

A2. Determine the values of p for which the series

n=1

lnn

np

converges.

done checked corrected study MT study final



4. Extra-Practice Questions:Try these questions for some more practice. The more practice you get the better you will understand thematerial and the better you will do on quizzes and exams.

(Stewart) Section 11.1: 1 - 55 (odd), 69, 71, 73 (Stewart) Section 11.2: 1 - 63 (odd) (Stewart) Section 11.3: 1 - 31 (odd)

Legend (for type of question):RE = Routine Exercise: This is something you should be able to do in your sleep ;-). Your goal is to beable to answer these questions quickly and accurately every time. These form the foundations of yourskill set.TC = Time Challenge: Speed and accuracy are important factors in solving this type of routine exer-cise. Try to do these exercises within the time limit, usually 5 minutes. If you need more time thanthat, its o.k., but keep practicing! Solving these routine exercises provides a foundation for solvingmore involved problems, and is essential in performing well on quizzes and exams.WP = Word Problem: Translating words into expressions (also known as modeling): Master this skillnow, we will be using this all term.CD = Concepts and Definitions: These questions relate to your understanding of the new languagewe are introducing. They should help you remember the important definitions and theorems.CE = Concepts and Explorations: This indicates a question which is testing your understanding of thefundamentals. It is not a routine exercise since the solution process may not be obvious at first glance.It may take a little bit of thought to figure out what to do, dont be afraid to play around with someideas. Youll learn more by making mistakes and taking routes which lead to dead ends. You must beable to do these types of questions to succeed in learning this material.HL = Higher Level Understanding: This indicates a question which is testing understanding at ahigher level. These questions will require more thought than a RE or CE so dont be discouraged ifyou cant see how to do this immediately. Perseverance and playing around with ideas is the key tothese questions. Understanding this material at this level is an expected outcome of this course.CM = Computer of Computational Device: This indicates a question in which a computer or calculatoris needed.

Selected Hints & Answers:

11.1: 28. converges to 011.1: 56. converges to 0. Make sure you can explain why?.11.1: 64. (a) divergent (b) convergent11.1: 76. decreasing and bounded between 0 and 1/e.11.1: 82. Use induction (similar to Example 14 in text). 3

5

211.2: 42. Do the terms get smaller (i.e. tend to zero)?11.3: 12. convergent11.3: 20. convergent11.3: 24. convergent

Additional questions:A1. (b) Can use induction (this is similar to Example 14 in section 11.1 of text, and question 82). However, it is not really necessary to use induction, you justneed to show an+1 > an for all n.(c) 4.A2. converges for p > 1 and diverges otherwise.


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