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X# œ 4py and y œ p Ê x# œ 4p# Ê x œ „ 2p. Therefore the line y œ p cuts the parabola at points (c2pß p) and (2pß p), and these points are È[2p c (c2p)]# b (p c p)# œ 4p units apart. 72. x lim Š b x c ba Èx# c a# ‹ œ Ä_ a œ b a x lim Ä_ ’ x # c ax # c a # b “ x b È x # c a# œ b a x lim Ä_ b a x lim Ä_ ’ Šx c Èx# c a# ‹ œ a# “ x b È x # c a# b a x lim Ä_ – Šx c Èx# c a# ‹ Šx b Èx# c a# ‹ x b È x # c a# œ0 Copyright © 2010 Pearson Education, Inc. Publishing as Addison-Wesley. — 687 688 Chapter 11 Parametric Equations and Polar Coordinates 73.

Copyright © 2010 Pearson Education, Inc. Publishing as Addison-Wesley. 4 Graphing in Polar Coordinates 30. Note that (rß )) and (crß ) b 1) describe the same point in the plane. Then r œ cos 2) Í c sin ˆ2() b 1)) b 1# ‰ œ c sin ˆ2) b 5#1 ‰ œ c sin (2)) cos ˆ 5#1 ‰ c cos (2)) sin ˆ 5#1 ‰ œ c cos 2) œ cr; therefore (rß )) is on the graph of r œ c sin ˆ2) b 1# ‰ Ê the answer is (a). 31. 33. (a) 34. (a) 32. (b) (c) (b) (d) (c) Copyright © 2010 Pearson Education, Inc. Publishing as Addison-Wesley. 5 AREA AND LENGTHS IN POLAR COORDINATES 1.

0082 cos ) 76. Mercury: r œ CHAPTER 11 PRACTICE EXERCISES 1. x œ t # and y œ t b 1 Ê 2x œ t Ê y œ 2x b 1 " # tan t and y# œ "4 # # 3. x œ and y œ " # sec t Ê x# œ " 4 tan# t sec# t Ê 4x# œ tan# t and 2. x œ Èt and y œ 1 c Èt Ê y œ 1 c x 4. x œ c2 cos t and y œ 2 sin t Ê x# œ 4 cos# t and y# œ 4 sin# t Ê x# b y# œ 4 4y œ sec t Ê 4x# b 1 œ 4y# Ê 4y# c 4x# œ 1 Copyright © 2010 Pearson Education, Inc. Publishing as Addison-Wesley. 699 700 Chapter 11 Parametric Equations and Polar Coordinates 5. x œ c cos t and y œ cos# t Ê y œ (cx)# œ x# 6.

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