# Math148 Homework Assignments

o These are the recommended homework assignments from the book. Keeping current with homework assignments is crucial to mastering this course.
o These assignments are provisional and may be amended during the course according to class needs. For this reason, I've left space for you to note any changes or comments .
o Your experiences with these exercises may vary – if you still feel shaky on an area; do a couple more similar questions. On the other hand, if you've mastered a topic and you don‟t feel challenged, move on harder questions. The review exercises at the end of each chapter are also good sources for extra practice.
o Some of the applied questions can be challenging at first – in some cases you may want to return to them later. Also, occasionally we may do part of a section, and return to do the rest later. Keep track of the ones you've done.
o Use the homework to develop good practices in structuring your work. See the worksheet guidelines for some ideas on how to do this.
o Do odd numbers unless otherwise specified. Some symbols to note:

o OO = “Every Other odd number”.
o More challenging exercises are marked by underlining. However, your experience may vary.

Appendix A – Expressions, and Exponents

Note: This appendix, and chapters 1 and 2, deals with review material. I won‟t be covering all these topics in class – particularly the appendix. You should use these exercises as a guide, and target those areas that you‟re weak on from the survey I handed out, and the self test.

 Section Notes Recommended Set Self Test Additional Test on basic algebra. You can use this to identify any weaknesses in algebra. It has questions on order of operations , factoring etc. 7-12 All 17-25 all 26- 28 29 31 32-37 all 39 40 42 46-49 all A-1 This is a basic true false quiz on order of operations . 7-25 odd A-2 Polynomials. Cover if you missed questions 7-12 in the Self test, or need distributive law review. 1 5 7 9 15 19 21 27 29 33 35 37 43 A-3 Factoring review . While all factoring is important, factoring expressions of one variable is most important for now. We'll do some more complicated factoring later. 1 5 7 9 11 13 15 19 23 27 31 35 39 41 43 A-4 Rational Expressions. You can leave 25 27 till later if you wish. 1 3 5 9 11 13 15 17 19 21 25 27 31 33 35 A-5 Review here if you've trouble with negative exponents. There's also some scientific notation. You can leave 43 till later if you wish. 1-13 odd 15 19 25 27 31 33 35 37 43 A-6 Rationals and Radicals. 83 85 and 87 you can skip for now, but they show the type of expression you need to use for calculus. 1 5 7 9 11 13 15 19 23 25-33 odd 35 37 39 41 43 55 57 67-70 all. 83 85 87 A-7 Quadratics. You can use this for extra practice before section 2-3. 1 3 5 7 9 13 15 19 21 23 25 27

Chapter 1 Homework

 Section Notes Recommended Set 1.1 A fundamental section. Solving linear equations is crucial to the course. We'll skip story problems for now, focus on algebra. 1 5 7 9 11 15 17 19 21 27 31 33 35 37 39 (By “graph” they mean just shade in a number line)  41 1-2 Lines. Hopefully easy. Questions 41 43 45 47 51 53 are important. We may return to applications later. 5 7 9 11 13 17 19 21 25 27 37 39 41 43 45 47 51 53

Chapter 2 Homework

 Section Notes Recommended Set 2-1 Functions! 1 3 5 9 11 13 15-20 all 21-29 all 33 35 39 41 45- 63 odd 65 67 69 77 79 91 93 95 97 101 103 105 107 109 2-2 Specific functions, transformations 1 3 5 7 9 13 17 21-41 odd 43 45 49 53 2-3 Quadratic functions. 1 3 5 7 9 11 15 19 21 23 25 27 29 35 37 39 43 2-4 Exponential functions. Read my handout first.  Remind me to talk about q37 39 55 – the graphs have special names. 1 3 7 13 15 17 19 21 23 27 29 31 33 37 39 43- 51 odd 55 57 61 67 75 2-5 Logarithmic functions . 1-77 odd 79 83 2 Review I‟m including a core review set. You can do  others for additional practice. 4 5 11 12 15 16 19 22 38 41 43 47 48 54 56 57 59 62 64-71 all 72 75 81 83

Chapter 3 Homework

 Section Notes Recommended Set 3-1 Limit idea Notation (including left and right limits). Familiar limits ( polynomials etc Limits using algebra Limits of difference quotients . 1-21 odd 23 27 31 35 37 39 41 43 47 49 55 57 3-2 Continuity Recognizing points of discontinuity on a graph. Continuous functions from formula. Open and closed intervals.  Where function is positive and negative  Where function increasing/decreasing. Side topic in q27,29 etc– solving quadratic and rational inequalities . Q 27 and 29 involve a small side track into solving inequalities. We‟ll do this graphically most of the time. 3-3 Infinite limits  For use in describing vertical  asymptotes. limits at infinity.  End behavior of functions. 1-8 all 9-15 odd 17 19 21 23 25 31 33 35 37-47 odd 51 57 59 51 is important in understanding how to remove a discontinuity. The function has hole, but by setting a appropriately we can “patch” the hole. 3-4 Derivative Average rate of change The derivative from the difference quotient. Finding it from first principles. Determining from a graph where the function is differentiable (without finding the value). 1 2 5-15 odd 19 25 29 30 31-38 all 39 47 49 3-5 Differentiation Power rule , polynomials 1-47 odd 49 51 53 57^G 61^G 69 71 75 81 83 The ones marked with a “G” require extra work on graphical calculator. We may skip first time through. 3-6 Differentials 11-21 odd 23 25 27 We’ll skip this entire section till later, and continue with derivatives… 3-7 Marginal Analysis Applying derivatives to cost analysis etc 1-15 odd There's a lot of formulas in this section . You should read the text and add to a note card if necessary before working on the examples. 3 review Page 210 1 3 5 7-9 all 10-16 all 23 25 32 33 39 43 55 57 59 61 65 67 72-75 85 93

Chapter 4 Homework

 Section Notes Recommended Set 4-1 All about e Applying to compound interest . 1-9 odd 11 17 25 1-9 odd 11 15 17 25 33 35 37 38 We may add extra applications. The current plan is to focus on exponential growth and decay. 4-2 Derivatives of log and exponential functions 1-21 23 27 29 31-41 odd 51 53 55 In 31-41, note that if the base is not e then you should use a different formula . 4-3 Derivatives of products and quotients 1-23 odd 39 41 43 45 47 49 51 53 55 59 61 63 67 69 71 73 75 83 85 87 4-4 Chain rule. The last big rule of differentiation. See my handout for the algebra you will need. for some of the higher numbered questions. 1-15 odd 17-35 Other odd 37 39 43 45 47 49 51 57 61 63 65 69 71 77 79 83 85 89 91 93 95 96 97 Some of these (eg 91) get quite messy, you may need to spent some time over a few nights doing them. 4-5 Implicit Differentiation Optional – we'll skip for now. 4-6 Related rates. Optional – we'll skip for now. 4-7 Elasticity of demand 1-11 odd 13 15 17 19 21 23 27 29 31 3941 43 4 review P. 272 3 9 11 13 17 25 29 35 41 43

Chapter 5 Homework

Note: I've underlined harder questions. Your experience may vary. Also, I may vary the assignments depending on class needs. This list is open to change.

 Section Topics and Notes Recommended set 5.1 Graphing using the first derivative. Note the book uses this idea called partition numbers as well as the critical values. In my opinion, the distinction is not important, and we'll just use the term „critical values. (Just so you know, critical values common terminology, but „partition numbers‟ is rare in my experience). 1-8 all 11-18 all 19-33 odd 39 41 43 47 49 51 55 57 59 63-68 all 69 71 75 79 79 81 83 85 97 5.2 Graphing using the second derivative. The second derivative measures the concavity of the graph. 1 2 3-6 all 7-17 odd 19 21 23 33 37 41 43 47 51 55 5.3 L'hopitals rule None – not covering for now. 5.4 Curve Sketching This section pulls together the ideas from 5.1 and 5.2. In class I'll give extra tips on how you can sketch graphs efficiently. 1 2 3 5 7 13 15 17 21 25 31 33 35 41 45 65 67 73 75 5.5 Absolute extrema.  The important point in this section is that if you're finding extrema on an interval that is closed or half closed, don‟t forget to check the end points – the derivative won‟t tell you about these. 1 3 5 7 9 11 13 15 19 21 27 29 31 35 39 41 45 51 55 5.6 Optimization - Story problems using graphing. 1 3 11 13 17 19 23 5 review P. 356 1-8 all 9 13 17 35 37 49 55

Chapter 6 Homework

 Section Notes Recommended Set 6.1 The idea of an "antiderivative" and the indefinite integral. 1-12 23 25 27 47 -71 other odd. 73 75 77 6.2 Integration by substitution Note carefully how I work the examples in class, and be prepared to think hard about these. Sometimes the correct substitution is hard to see. 1 3 7 9-23 odd 25 27 29 31 33 (these are harder). 5.3 Differential equations We'll skip this section. 6.4 Definite Integral This Section covers a lot of theory. We'll just do the basic idea, and skip the details. 17-27 odd 29 31 33 35 6.5 The fundamental theorem of calculus. Calculating definite integrals Average value applications. Doing integration on your calculator. 5-29 odd 41 43 45 63 73 6 review 1 3 5 19 21 23 33 35 36

Chapter 7 Homework

 Section Notes Recommended Set 7,1 Applications of integration to area. 7 – 23 odd 25 27 29 35 – 47 odd 57 61 63 65 69 71 7,1 A range of applications Probability Continuous income stream and future values of it. Producers and consumers surplus. To be determined – we'll do a selection of the applications here.
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