For each of the following, sketch the trace of (, R), describe its orientation, and verify that it is a subset of the surface S a) (t) (3t, 3 sin t, cos t), S (x, y, z) y2 9z2 9 b) (t) (t2, t3, t2), S (x, y, z) z x c) (t) (t, t2, sin ), S (x, y, z) y x2 d) (t) (cos t, sin t, cos t), S (x, y, z) y2 ...

a Let x y z t Then y 2 9z 2 9 sin 2 t 9 cos 2 t 9 The trace spi ...

For each of the following, sketch the trace of (, R), describe its orientation, and verify that

Question:

For each of the following, sketch the trace of (ɸ, R), describe its orientation, and verify that it is a subset of the surface S.
a) ɸ(t) = (3t, 3 sin t, cos t), S = {(x, y, z) : y2 + 9z2 = 9}
b) ɸ(t) = (t2, t3, t2), S = {(x, y, z) : z = x]
c) ɸ(t) = (t, t2, sin*), S = {(x, y, z):y = x2}
d) ɸ(t) = (cos t, sin t, cos t), S = {(x, y, z) : y2 + z2 = 1}
e) ɸ(t) = (sin t, sin t, t), S = {(x, y, z) : y = x}