Calculate s f(x, y, z) dS for the given surface and function. D(r, 0) = (r cos(0), r sin(0), 0), 0

Q: 5. Find an equation plane to the surface (u, v) = (3 cos(u) sin(v), 2 sin(u) sin(v), cos(u)) at the…

A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

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Q: - Let f(x, y) =sin(x y − x − 3y+3). (vi) Which of the surfaces below is a graph of this function?

A: Given .This can be rewritten asOn the xy−plane, , if  gives us hyperbolas on the xy−plane.

Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given…

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Q: 2. § F•dï , where F = (ycos(x) – xy sin(x), xy + xcos(x)) and C is the C triangle from (0,0) to…

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

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Q: Consider the function (a) Find z = 3e- cos x + 2e* siny. 8²% Әхду 8²z дудх -(0,0) -(0,0) and (b)…

A: Function: z=3e-ycos x+2exsin y To find: a)  ∂2z∂x∂y0,0 and ∂2z∂y∂x0,0 b) The slope of the surface…

Q: z = sin(2x) cos(y) 1. Construct a grid for x and y going from (0, 0) to (4, 6). 2. Use this grid to…

A: Using the Geo Gebra software I have plotted all these three problem in 3d graph. 1. The grids are…

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Find an equation of the tangent plane at P = 4x² + z²e-x = 25 13/1) 2,3, to the given surface.…

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Q: Find V (V x F) if F(x, y, z) = 8 sin xi + 6 cos(2.x - 3y)j + 7zk. %3D | V. (V x F) =

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Q: Evaluate F dr where C is the line segment from (7,-,1) to (20, 1, and F (sin(yz) + 1)i + (zz cos(yz)…

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