Consider the parametric surface 𝑆:𝑟⃑(𝑢,𝑣)=〈sin𝑢cos𝑣,sin𝑢sin&#119

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Consider the parametric surface 𝑆:𝑟⃑(𝑢,𝑣)=〈sin𝑢cos𝑣,sin𝑢sin&#119

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Consider the parametric surface
𝑆:π‘Ÿβƒ‘(𝑒,𝑣)=〈sin𝑒cos𝑣,sin𝑒sin𝑣,cos𝑒βŒͺ with 0≀𝑒 ≀ πœ‹/3, 0≀𝑣≀2πœ‹.
(a) Find the scalar equation of the tangent plane to 𝑆 at the
point (πœ‹
4,πœ‹). Answer: βˆ’π‘₯+𝑧=√2
(b) Find the surface area of 𝑆. Answer: πœ‹
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