 
Summary: Math 2210 Key 7
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Problem 1 For each of the following curves, sketch the curve showing the orientation
generated by the parameterization, state if the curve is closed (yes/no) and if it is
closed state if it is oriented positively or negatively.
(i) C1 : r1(t) = (cos(t), sin(t)), 0 t ,
1
1 1
1
Not closed
(ii) C2 : r2(t) = (3sin(t), 2cos(t)), 0 t 2,
Closed;
negative
(iii) C3 : r3(t) = (2 + cos(t), 2 + sin(t)), 0 t 2,
Closed;
positive
1
(iv) C4 : r4(t) =
ti + tj 0 t 2
(2  t)i + 1
