x (b) Hyperbolic paraboloid. M: z = a Show that M is covered by the single patch х(и, v) — (а(u+ v), Ы(u — v), 4uv) on R*.

Q: Compute foxy dx + (x³/2+y³/2) dy where C is the square with vertices (0,0), (0,1), (1,1) and (1,0)…

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Q: Given the inner product space (R³(R),+,.,-), where oy = 3x₁₁ + 2(x₂₁ + X₁3₂) + 3x₂y₂ + 2X3Y3, X =…

A: This is a problem related to inner product space. Please see the next step for details.

Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

Q: 219. The diagram at right shows a rectangular solid, two of whose vertices are A = (0, 0, 0) and…

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Q: Shouldn't the center of (r – 3)² = 1 25 (y – 5)² 4 be (5, 3)?

A: We have to verify that if center of given hyperbola is 5, 3 or not where equation is given as:…

Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Here we are given a 3d surface S by the following equation : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

Q: Use the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first…

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Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2)…

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Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2 m(PB) (2) Convert the…

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Q: 2 2xy) dy, v es (0, 0), (2, 0), (

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Q: T:R3⟶R3 with T(v1,v2,v3)=(v1+v2,v2+v3,v3). Find the  a. image of v=(−2,1,2)  b. pre-image of…

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