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at the indicated points:
(b) σ(r, θ) = (r cos θ, r sin θ, 2θ), P =
√
3, 1,
π
3
σ(u ,v) = (sech u cos v, sech u sin v ,tanh u)
is a regular surface patch of the unit sphere
σ(u, v) = (sech u cos v,sech u sin v,tanh u)
is a regular surface patch of the unit sphere
Sketch the level curves f−1(c) for the following functions:
f(x, y, z) = x − y2 − z2, c = −1, 0, 1.
(a) f(x ,y) = x^2 + y^2.
1(c) for the following functions:
f(x, y, z) = x-y2-z2
, c = 1, 0, 1
Sketch the level curves f−1(c) for the following functions:
(a) f(x, y) = x2 + y2, c = 0, 1, 2, 3, 4.
(b) f(x, y, z) = x − y2 − z2, c = −1, 0.
Prove them
K=|r'×r"|/|r'|^3
T=[r', r",r"]/K^2(r')^6
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#340153 on Dec 2023