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C-4 Appendix C MINI PROJECT Drawing Conclusions from Visual Evidence This discussion concerns x-intercepts and requires that at least one person in the group have a graphing utility. How much graphical evidence do you feel is necessary before you are “reasonably certain” about the exact value of an x-intercept? Or would graphical evidence alone never leave you reasonably certain? To focus the discussion, begin by considering the two views of the graph of the equation y x 3 550x 11 in Figures A and B. 10 0 _10 _20 _30 _40 _0.10 _0.08 _0.06 _0.04 _0.02 0.00 Figure A Close-up view of y x 3 550x 11 near an x-intercept. The intercept is either 0.02 or something very close to that. 5 0 _5 _10 _15 _20 _0.05 _0.04 _0.03 _0.02 _0.01 0.00 Figure B Still closer view of the x-intercept in Figure A (zooming in by a factor of 2). Would you say now that it is quite likely that the intercept is exactly 0.02?
Appendix C C-5 MINI PROJECT Thinking About Slope Working within a group or with the class at large, carry out the two activities indicated below. Then, on your own, write a summary of what you have learned. 1. What if the definition of slope that we gave in this section had instead been m y 2 y 1 ? Try reworking Example 1* using this version of slope and x 2 x 1 describe what happens. Why is this unsatisfactory? 2. Why, where, and when did the use of the letter m for slope originate? See what you can find out by reading comments from mathematicians and math historians at the following Internet website: http://mathforum.org Select the Math Talk tab, then click on the Discussion Groups link, and search on the word slope. As with many historical issues in many fields, don’t expect one simple definitive answer. Summarize what you find out. *Example 1 of Section 1.6, Precalculus: A Problems-Oriented Approach, 7th edition
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Page 7 and 8: Appendix C C-7 1. equilateral trian
Page 9 and 10: Appendix C C-9 MINI PROJECT Flying
Page 11 and 12: Appendix C C-11 MINI PROJECT An Ine
Page 13 and 14: Appendix C C-13 (a) The two data po
Page 15 and 16: Appendix C C-15 and http://www.svob
Page 17 and 18: Appendix C C-17 For Figure D we can
Page 19 and 20: Appendix C C-19 MINI PROJECT A Grap
Page 21 and 22: Appendix C C-21 MINI PROJECT Who Ar
Page 23 and 24: Appendix C C-23 MINI PROJECT 1 How
Page 25 and 26: Appendix C C-25 either the quadrati
Page 27 and 28: Appendix C C-27 PROJECT The Least-S
Page 29 and 30: Appendix C C-29 Then, for any line
Page 31 and 32: Appendix C C-31 PROJECT Finding Som
Page 33 and 34: Appendix C C-33 3. When a person co
Page 35 and 36: Appendix C C-35 2. Use part (b) of
Page 37 and 38: Appendix C C-37 PROJECT Coffee Temp
Page 39 and 40: Appendix C C-39 MINI PROJECT More C
Page 41 and 42: Appendix C C-41 The calculations co
Page 43 and 44: Appendix C C-43 PROJECT Transits of
Page 45 and 46: Appendix C C-45 E A ¨ V ¨ Bª d S
Page 47 and 48: Appendix C C-47 PROJECT A Linear Ap
Page 49 and 50: Appendix C C-49 Continuing with the
Page 51 and 52: Appendix C C-51 PROJECT Constructin
Page 53 and 54: Appendix C C-53 1 y Figure A A grap
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Appendix C C-55 PROJECT Fourier Ser
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Appendix C C-57 sine and cosine fun
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Appendix C C-59 PROJECT The Motion
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Appendix C C-61 PROJECT The Design
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Appendix C C-63 denote the angles o
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Appendix C C-65 inverse trigonometr
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Appendix C C-67 PROJECT Inverse Sec
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Appendix C C-69 Alternatively, usin
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Appendix C C-71 PROJECT Snell’s L
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Appendix C C-73 vertically downward
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0 0 0 Appendix C C-75 PROJECT Vecto
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Appendix C C-77 Exercise 8 We outli
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Appendix C C-79 y y=2x+5 Îy=2 A (1
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 Appendi
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Appendix C C-83 PROJECT Parameteriz
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Appendix C C-85 It is worth noting
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Appendix C C-87 6. Show that the li
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Appendix C C-89 2. An altitude of a
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Appendix C C-91 PROJECT The Leontie
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Appendix C C-93 n x units of that
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Appendix C C-95 him/herself through
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Appendix C C-97 PROJECT The Leontie
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Appendix C C-99 As in the solution
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Appendix C C-101 MINI PROJECT 2 Con
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Appendix C C-103 PROJECT Using Hype
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Appendix C C-105 PROJECT Two Method
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Appendix C C-107 (b) Use Method 1 t
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Appendix C C-109 MINI PROJECT An Un
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Appendix C C-111 PROJECT More on Su
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Appendix C C-113 SOLUTION 25 25 a (
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Appendix C C-115 4. Simplify the fo
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