64 Chapter 2. Functions, Limits, and Continuity (a) Sketch the surfaces. (b) Give a rigorous argument (not merely based on your pictures) that every pair of point be joined by a curve in X but that the same is not true of Y. 11. Consider the function Th 0-F (2+cos t) cos s -C0 (2+ cos t) sin s 0 S,t<27 sin t (a) Sketch the image, X, of g. *(b) Find an algebraic equation satisfied by all the points of X. SO 12. Consider the function (defined wherever st 1) Fi re 0-B T+15 st-1 S S-t (S t st-1 m 1+S st-1 fr

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64
Chapter 2. Functions, Limits, and Continuity
(a) Sketch the surfaces.
(b) Give a rigorous argument (not merely based on your pictures) that every pair of point
be joined by a curve in X but that the same is not true of Y.
11. Consider the function
Th
0-F
(2+cos t) cos s
-C0
(2+ cos t) sin s
0 S,t<27
sin t
(a) Sketch the image, X, of g.
*(b) Find an algebraic equation satisfied by all the points of X.
SO
12. Consider the function (defined wherever st
1)
Fi
re
0-B
T+15
st-1
S
S-t
(S
t
st-1
m
1+S
st-1
fr
Transcribed Image Text:64 Chapter 2. Functions, Limits, and Continuity (a) Sketch the surfaces. (b) Give a rigorous argument (not merely based on your pictures) that every pair of point be joined by a curve in X but that the same is not true of Y. 11. Consider the function Th 0-F (2+cos t) cos s -C0 (2+ cos t) sin s 0 S,t<27 sin t (a) Sketch the image, X, of g. *(b) Find an algebraic equation satisfied by all the points of X. SO 12. Consider the function (defined wherever st 1) Fi re 0-B T+15 st-1 S S-t (S t st-1 m 1+S st-1 fr
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