R = {(x,y) E R ×x R : x > y} T = {(x, y) E R × R : x > y}. RoT.

Q: IX. Į F dF where F = (x,y) and C is the straight line from (2,3) to (4,0)

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Q: Find fa, fy, fyx and fy if f(x, y) = x + y + xy ух

A: This is second partial derivative so do the derivative like normal considering all other variable…

Q: af af Given f(x, y) = 2x²+ 2xy + y² + 4x - 8, find all points at which = 0 and ах = 0…

A: Step 1: Objective and ConceptObjective:-To determine the points at which the partial derivative of…

Q: Find fyx. zyx 5,6 3 f(x, y, z) = x³y2³ + xy + yºz z

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Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: , (х, у) (0,0) x+y f(x.y)%3D (х, у) (0,0)

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Q: y" + 2y²+2=0 Find y(x), then simplify y" + 2y + 2 = 0

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Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: What is the domain of h(x, y) = Vx - y?

A: Given: hx,y=x-y we know that for domain of square root function inside of root not has to be greater…

Q: An equation of the line tangent to the graph of f(x) = -x(1 – 2x)³ at the point (1,1) is a. y = -7x…

A: f(x) = -x (1-2x)3  f'(x) = -3x(1-2x)2 (-2) + (1-2x)3 (-1) f'(1) = 6(-1)2 +1 f'(1) = 7   Slope m = 7…

Q: Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

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Q: af and . Given f(x, y) x'+ y find dx ' dy' axdy дудх

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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: af af Given f(x, y) = 2x² + 2xy + y² + 8x - 3, find all points at which = O and дх ду (x, y) - ( [ =…

A: To find the points where both df/dx and df/dy are zero, we first need to compute the partial…

Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: For f(x, y, z) = x² - y² + z², find f(2, -1, 4).

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Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: Ut +Uxx =0 , Uxl0,t) =0, t7. Ux (1,f) = 0, t70 O<a<M, tro. UC2, 0)

A: The heat equation with Neumann boundary conditions is as follows. ut=c2uxx, 0&lt;x&lt;L,…

Q: [x, y]²=[-1,0]=-1

A: We have [x,y]^2=[-1,0]=-1