Let G(x, y, z)= (1+9xy)2 and consider a surface S given by the parametrization r(u, v)= [u, u, v], 0sus1, -1

Q: Does there exist a surface x(u, v) such that E=G=1,F=0 and L=1,M=−1,N=0?

A: The objective of the question is to determine if there exists a surface x(u, v) that satisfies the…

Q: Evaluate the line integral x¹ z ds, where C is the line segment from (0, 7, 5) to (7, 1, 2). C

A: We have to evaluate  where  is the line segment from  to

Q: Find Əz ?х Əz da Əz ду = ab brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)). • Put…

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Q: 49. Let f(x, y, z)=sin(x² + y² +2²). (a) Describe in words the shape of the level surfaces of f. (b)…

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Q: 1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux…

A: Consider the given information: The given surface is  z=h-x2-y2,     h>0z=0 Also F→=x2, y2, z2 To…

Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

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Q: Consider the equation of the surface S given by -2X“ - yPz° + xy = -4, where a is an odd number and…

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Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: Determine the point(s) on the surface z = e(3x² +9y2) at which the tangent plane is parallel to the…

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Q: Advanced Math 4. Let f: S^2 → S^2 be a reflection of the sphere which leaves the plane H = {(x, y,…

A: Given Plane : H =x,y,z100x +239x+11z=0 To find: All great circles which are invariant under f.

Q: Prove that at the point of intersection of the surfaces x² + y² = 2², z = a tan` X where y = x tan…

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Q: Find the directional derivative of f(x, y) = In(e"- 3y) at the point (0,0) in the direction of 3i +…

A: We are asked to find directional derivatives of function.

Q: Given the surface f(x, y) = -+2 ln y, and the point P = (-1, 3) 4 -) Find the rate of change of fat…

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Q: 3. Consider the surface S={(x, y, z)| = = e`(x²+x²) – e¯ªª, (x² + y²) ≤a²}. Use a simple way to…

A: Given surface S is S=x ,y,z  z=e-x2+y2 , x2+y2≤a2 To Find : Vector Area of S.

Q: Find symmetric equations of the normal to the surface, r (u, v) = at a point (1, 1, 3

A: given ru,v=<u2,v2,u+2v> therefore ru=∂∂uu2i+∂∂uv2j+∂∂uu+2vk=2ui+0j+k…

Q: Let z = g(x, y) = f(3 cos(ry), y + e²") provided that f(3,5) = 7, f1(3,5) = 2, f2(3, 5) = 5. i) Find…

A: The function given z=gx,y=f3cosxy,y+exy;f3,5=7,f13,5=2,f23,5=5. i. Find g10,4

Q: Let S be a surface described by x² + y² + 32² = 1, z ≤ 0, and let F(x, y, z) = yi-xj+zx³y²k. Prove…

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: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

Q: Consider the statements about the surface of equation: n²y z = y² sin x + and the point P (1, 2) in…

A: Directional derivative of a function f(x,y,) in the direction of unit vector  u^ Dux,y=∇f.u^…

Q: Verify the statements and formulas 41. The coordinates of the centroid of a differentiable plane…

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Q: Let C be the curve of intersection of the surfaces y = V2 x2 and z 2/2 ху. (a) Compute the curvature…

A: Given C be the curve of intersection of the surfaces y=2x2 and z=223xy

Q: Determine if F(n.y,z) =x+y+Z have a maximum/minimum value when m,9, z) lies on unit sphere:x'+yiZ=1•…

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Q: Let z = f(x, y) = x^2 + 4y^2, and consider the z-value 16. Find the level set for the z-value 16,…

A: Here is the solution of the given problem.

Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is

Q: Let f(x,y,z)=-x^2+sin(y)-2z^2=0 define a surface in 3 dimensions. Find the equation of the normal…

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

Q: Evaluate the line integral F.dr. where F(x, y, z) = (5x² + 6y) î — (3x + 2y²)j + 2xz²k, and C is…

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Q: Find the surface normal vector to the surface z 4-(x +y²) at the point (1, 1,v2) by (a) Vf (b) N =…

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Q: Determine the area of the parametric surface S with equation R(u, v) = (u²+v², 2uv, u²_v²) where 0 ≤…

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