Engineering Calculus Notes 323

Engineering calculus notes 323

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Unformatted text preview: 311 3.5. SURFACES AND THEIR TANGENT PLANES which corresponds to π 3 π θ=− . 4 φ= The partials are → ∂− π π p ,− ∂φ 3 4 → ∂− π π p ,− ∂θ 3 4 → π π− → + cos π sin − π → − − sin π − ı k cos − 3 4 3 4 3 √ → 1→ 3− 1→ k ı = √ −− √ −− 2 22 22 π π → − + sin π cos − π → − = − sin sin − ı 3 4 3 4 √ √ 3→ 3→ =− √ − + √ − ı 22 22 = cos so a parametrization of the tangent plane is given by √ √ 1 3 3 √ √ △s △r + x= √ + 22 22 22 √ √ 1 3 3 √ √ y=− √ − △s △r + 22 22 22 √ 3 1 z= + △r ; 2 2 to find...
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