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Engineering Calculus Notes 323

Engineering Calculus Notes 323 - 311 3.5 SURFACES AND THEIR...

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3.5. SURFACES AND THEIR TANGENT PLANES 311 which corresponds to φ = π 3 θ = π 4 . The partials are −→ p ∂φ p π 3 , π 4 P = p cos π 3 cos p π 4 PP ı + p cos π 3 sin p π 4 PP p sin π 3 P k = 1 2 2 ı 1 2 2 3 2 k p ∂θ p π 3 , π 4 P = p sin π 3 sin p π 4 PP ı + p sin π 3 cos p π 4 PP = 3 2 2 ı + 3 2 2 so a parametrization of the tangent plane is given by x = 3 2 2 + ± 1 2 2 ² r + ³ 3 2 2 ´ s y = 3 2 2 ± 1 2 2 ² r + ³ 3 2 2 ´ s z = 1 2 + ³ 3 2 ´ r ; to Fnd an equation for the tangent plane, we compute the normal N = ³ 1 2 2 ı 1 2 2 3 2 k ´ × ³ 3 2
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