(a) Consider the surface M having the parameterization given by f(s, t) = over the region in the st plane bounded by s = 1, s = 2 and the curves t = s2 and t = 6 - s. Set up the double integral (with appropriate limits on the integrals) which represents the surface area of M.   (b) Let g(x, y, z) = y + xz. Set up the integral ∫∫gdσ over the surface M. Do not evaluate

Q: Show that the curve r= Vti + Vtj + (2t – 1)k is tangent to the surface x +y² – z = 1 when t=1

A: Given that r=ti+tj+2t-1k and f=x2+y2-z-1 Take the derivative for f, ∇f=ddx,ddy,ddzf=2x,2y,-1…

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A: The given surface is:ϕ(u, v)=u2+v, u, v

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A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

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Q: ve = Vti + Vrj + (2t – 1)k is tangent to the surface x+y-z = 1 Show that the curv when t=l

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A: ∫S∇×F·dS=∫S∇×F·n^dS=ijk∂∂x∂∂y∂∂zy-xzx3y2=i2zx3+j-3zx2y2+k-1-1∵z≤0∴n^=-k∫S∇×F·n^dS=∬i2zx3+j-3zx2y2+k-…

Q: Let f(x, y, z)=²—4y². (a) Describe the domain of f. (b) Describe the level surface f(x, y, z) = 2.…

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Q: Calculate SS dxdy D (x+y)² in Surface D limited to curve y=x² and the lines 2 Y=x+2 and x = 1.

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

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A: Given the surface fx,y,z=-x2+siny-2z2=0. Let us find the equation of the normal to the surface in…

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