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and r = 2 + cos 20. 11. Referring to example 11 of 10.3 to study the family of curves r = 1 + csin 0. Here we restrict oursleves to the case 0 1 there is a loop that decreases in size as c decreases. When c = 1 the loop disappears and the curve becomes the cardioid that we sketched in Example 7. For c between 1 and ; the cardioid's cusp is smoothed out and becomes a "dimple." When c Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andfor Chapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning rese the right to remove additional content at any time if subsequent rights restrictions require it 666 CHAPTER 10 Parametric Equations and Polar Coordinates In Exercise 53 you are asked to prove decreases from ; to 0, the limacon is shaped like an oval. This oval becomes more analytically what we have discovered circular as c -> 0, and when c = 0 the curve is just the circle r = 1. from the graphs in Figure 19. c =1.7 c=1 c=0.7 c= 0.5 c=0.2 c=2.5 C=- C=0 c=-0.2 c=-0.5 C=-0.8 FIGURE 19 Members of the family of The remaining parts of Figure 19 show that as c becomes negative, the shapes limacons r = 1 + c sind change in reverse order. In fact, these curves are reflections about the horizontal axis of