MATH235 FALL 2009

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• Syllabus
  
  
• Mathematical Notation and Concept Sheet
  
  
• Basic Properties of Algebra
  
  
• 4 Limit Proofs
  
  
• 3 More Limit Proofs
  
  
• Limit Tool Sheet
  
  
• Pinching Theorem Proof
  
  
• Trig Limits Worksheet
  
  
• Product Rule for Differentiation Proof
  
  
• Chain Rule for Differentiation Proof
  
  HOMEWORK ASSIGNMENTS:
  
  8/24: Section 2.3 #1,3,7,9,11,13. Also, prerequisite skills diagnostic on Ch.1 material tomorrow!
  
  8/28 Section 2.3 #37, 38, 47, 51, 55, 59. Note that the first three problems are proofs!
  For #55, translate this problem as a limit as x approaches c of f(x): What is c, f(x), and L? What value of epsilon is given in the problem? What should delta be so that the cylinder is made within the acceptable error tolerance?
  
  8/31 Section 2.3 #45, 46. Note, these may look harder than the linear ones, but they're not! HW on (real) nonlinear proofs coming tomorrow!
  
  9/1 Section 2.3 #39, 43, 44. Also, for f(x)= x^2+3x-1, prove: The limit as x goes to 2 of f(x) is 9.
  
  9/2 Section 1.1 #1-5, 14-16 and Section 1.2 #5,7,9,11 to Review some basic Algebra!!
  Also Finish previous 2.3 HW assignments!
  Finally, look over your diagnostic test and return to me on Friday. Recall, each problem had a possible score of 0,1,2,or 3. We will review trig, exponential, and logarithm ideas in class as they present themselves. You should review basic algebra problems on your own that you had trouble with on the diagnostic test. Recall that Algebra Boot Camp is still running tonight and tomorrow night 6-8pm in Roop 200! In addition of course, Roop 200 is also available during its regular hours to help you.
  
  
• Quiz #1 Solutions
  
  9/4 Section 2.3 #42, 49, 52, 60(b). AND, for more algebra review do:
  Section 1.1 #57, 58. Section 1.2 #15-17, 49(a)-(f).
  
  9/7 Section 2.2 #1, 3, 5, 9, 55, 56, 57. ALSO, Quiz #2 tomorrow: a non-linear delta-epsilon proof!
  
  9/8 Read for understanding each of the following:
  (1) The Proof of the Sum Rule in Example 6, p. 79.
  (2) The Proof by Contradiction in Example 7, p.80.
  (3) The Proofs labeled 5 and 6 at the "3 More Limit Proofs" link above.
  You may also want to review the "Proof by Contradiction" information on p. 2 of the "Mathematical Notation and Concept Sheet" at the link above.
  FINALLY ( it should go without saying!) Finish any HW previously assigned that you do not have completed!
  
  
• Quiz #2 Solutions
  
  9/9 Section 2.2 #11-21 odd, 29-39 odd, 58, 83, 85.
  
  9/11 Section 2.2 #69, 70(a), 81, 82, 86. Also, READ to shake the cobwebs: Section 1.3 and Appendix 4: Trig Review!!
  
  9/14 Section 2.2 #47-52 (show steps applying our Limit Laws!), #68, AND Section 1.3 #1.
  AND Finish Trig Limits Worksheet from Class Today. It might be worth printing off a clean copy from the link above and working through it again, this time without so much erasing and/or crossing out! :)
  
  9/15 Section 2.4, #21, 22, 23-35 odd
  AND Section 1.3, #5-15 odd, 19, 31-38, 43, 45, 48, 49.
  
  9/18 Section 2.4, #1, 3, 5-7, 10, 13, 14, 17, 67. Also, for #77 and 78, simply write what limit statement the delta-epsilon description would correspond to. READ Section 2.4 as well (should go without saying...)
  ALSO, Quiz #3 next week (Mon. or Tues.) on HW from 9/7 - 9/15, excluding 9/8!
  Test #1 will be Tues. Sept. 29!!
  
  9/21 Section 2.4, #75, 76, and also Prove: lim as x goes to -infinity of 1/x = 0. Use our proof in class as a model for how to do these. The "proofs" in Example 6 in the book are lame, and are not really proofs!
  Quiz #3 tomorrow! Be sure you can do the HW from 9/7 - 9/15 (excluding 9/8) without needing tables or calculators!
  
  9/22 Section 2.4, #37-43 odd, 51-65 odd, 71, 73, 83.
  AND Section 2.5 #1-23 odd, 39, 41, 48, 51, 54
  
  9/23 Finish all HW above, and be ready to ask any HW questions on Friday 9/25. Test #1 will cover all material above through Section 2.5. On Monday we will start Section 2.6, but that will not be on Test #1.
  
  9/25 STUDY!!!!!!
  
  
• Quiz #3 Solutions
  
  9/28 KEEP STUDYING. You will have HW for Tu 9/29 on Section 2.6.
  
  9/29 TEST #1
  AND HW Section 2.6, #1-10, 13-19 odd, 23-29 odd, 30, 35, 39, 45, 61, 62
  
  9/30 Section 2.2, #25, 27, 41, 43, 45, 53, 67
  AND Section 2.4, #11, 12, 15, 74, 84
  AND Section 2.6, #21, 46, 50.
  
  10/2 Section 3.1, #3, 5, 7, 11, 19, 23, 25, 26.
  
  10/5 Section 3.1, #17, 27-32, 37-42, 45b.
  
  10/6 Finish the proof of the reciprocal rule that we started in class. That is, Let f(x) be a differentiable function and let g(x)=1/f(x). Use the limit definition of derivative and the definition of continuity to show that g'(x)= -f '(x)/[f(x)]^2. How does continuity play a role?!?
  ALSO, be ready for our quiz tomorrow on Section 3.1 HW type problems: computing derivatives from the two boxed limit definitions on pp.125-6 and writing the equation of a tangent line to a curve at point (in point-slope form!).
  
  10/7 Section 3.2, #1, 3, 7, 9, 11, 25 (simplify first!), 37, 39 (simplify first!), 47(d), 49(a),(c), 50(a), 53, 54, 55(a), 57, 58, 64.
  
  10/9 Section 3.2, #13, 17, 19, 21, 47(a)-(c), 51, 60(b), 63, and go back and read Examples 4 and 5 from Section 3.1 again. Finish all HW and be ready for a few brief HW questions and lots of new material on Monday!
  
  
• Quiz #4 Solutions
  
  10/12 Section 3.2, #5, 23, 24, 27, 28, 35, 43 AND Section 1.4, #5, 6, 21, 22, 24
  
  10/13 Section 3.4, #1-27 odd, 31, 35-45 odd, 47-50, AND Read the caution about derivatives of trig functions using degree measure instead of radian measure in #58!
  
  10/14 Section 3.3, #21, 22, 25, 26, 28, 29 AND Fill in all the blanks in the Chain Rule for Differentiation Proof Handout at the link above (handed out in class).
  
  10/16 Section 3.5, #5, 7, 9, 15, 17, 21, 23-29 odd, 35-41 odd, 47, 53, 55, 65, 73, 79(a), 109, 110, 115, 117, 118, and Re-read Examples 7 and 8.
  ALSO, turn in Chain Rule for Differentiation Proof Worksheet on 10/19 for a Quiz grade.
  
  10/19 Section 3.6, #9, 11, 13, 17, 19, 31, 35, 39, 40, 42
  AND Section 3.5, #13 AND Section 3.2, #29, 31.
  
  10/20 Section 3.9, #1, 3, 8(a), 10-13, 15-17, 19-21, 23, 26, 29, 34
  
  10/21 Section 1.5, #1-8, 29, 33-39 odd, 43, 67
  AND Section 3.7, #11, 15, 19, 21, 25, 27, 29, 37, 55, 61
  ALSO, Test #2 will be Weds. Oct. 28!! Plan to come 5-10 mins. early and stay 5-10 mins. late. Test #2 will cover material from 9/28 thru 10/26.
  
  10/23 Section 1.5, #27, 31, 41, 45, 49 AND Section 3.2 #33
  AND Section 3.7, #63, 67, 71, 75, 83, 85, 89, 93, 95
  ALSO, turn in Section 3.6 #40 on 10/26 for a Quiz grade.
  
  10/26 Section 3.7, #13, 33, 35, 51, 53, 65, 69, 73, 81, 87, 91, 98.
  Hint for #98: Start with e=(lim as h goes to 0) of (1+h)^(1/h). Then, what is e^x and why? Now let n=x/h (x is an arbitrary, but fixed, positive number) and convert the limit to the new variable, n!
  
  10/30 Section 4.1, #3, 7, 9, 11-14, 17, 34, 35, 37, 41, 43, 47, 51, 57, 59, 63, 65, 71, 72.
  
  11/02 Section 4.2, #1, 5, 7, 8, 10, 23, 26, 27, 29, 35, 46, 49, 68.
  
  11/03 Section 4.3, #3, 5, 7, 15, 17, 21, 23, 25, 31, 41, 43, 47, 49, 54, 55, 59.
  Feel free to ignore the part of the directions that say "Support your findings with a graphing calculator or computer grapher."
  
  11/04 Section 4.4, #1, 3, 15, 23-31 odd, 35, 41, 63, 65, 67-70, 75-83 odd, 82.
  
  11/06 HW: Get caught up on ALL Chapter 4 HW!!!! Be prepared for a new assignment on Monday when we hit Section 4.5: Optimization Problems. Your favorite, calculus word problems!!!
  
  11/09 Section 4.5, #2, 7, 9, 10, 12-15, 19, 20-23, 27, 41, 45, 49, 50a). One of these problems will be on Test #3!
  
  11/10 Section 4.8, #5a, 11a, 17a, 19a, 21a, 22a, 25-59 odd, 63-69odd, 77.
  
  11/11 and 11/13 Section 1.5, #9, 10, 51, 53, 69
  AND Section 3.8, #1, 15, 23, 29, 31, 33, 35, 43, 48, 49, 51, 54
  AND Section 4.1 #53 and Section 4.5 #39
  AND Section 4.8, #23, 61, 62, 79, 80, 87, 95, 11, 125.
  
  11/13 Get yourself caught up on all HW from 10/30 thru 11/13. Get organized for our test on Fri. 11/20! You've got LOTS of results to keep straight!!! On Monday, we'll jump right in to Chapter 5.
  
  11/16 Section 5.1, #1, 3, 5, 7 and Section 5.2, #29, 31.
  
  11/17 Section 5.3, #1-25 odd and Section 5.4, #41-49 odd, 75, 79a-c,f,g
  
  11/18 Section 5.4, #1-13 odd, 19, 23-31 odd, 51, 55, 57, 59, 69, 71, 72
  AND Section 5.3, #55 and #59 (Use the FTC to evaluate the associated definite integral!)
  
  11/20 TEST #3 ON everything from 10/30 HW through 11/13 HW. Test #3 will NOT cover Ch. 5 material (but the FINAL EXAM will!) Over Thanksgiving Week Break, you should be sure to READ Sections 5.1-5.4 and be caught up on the HW assignments over these sections as well! I'll take HW questions on 5.1-5.4 material on M 11/30 only!
  
  

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