Show that F is conservative and find a function f such that F= Vf, and use this result to evaluate F dr where C is any path from A(x. Vo) to B(x1, y1). F(x, y)= (6-8yli+(4x³y-12rylj: A(1, 2) and B(2, 2) o SFér=-12 O [F dr=-96 F-dr=-274

Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96,…

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Q: Compute the discriminant D(x, y) of the function. ƒ(x, y) = x³ + y4 − 6x − 2y² + 2

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Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: Determine whether F is conservative. If so, find a functionf such that F= Vf. F(x, y) = (16z-24xy…

A: Given  F→x,y=16x3−24x4ye−6xyi-24x5e−6xyj Let M=16x3−24x4ye−6xy and N=−24x5e−6xy Differentiate…

Q: q³ + p Consider the function f(p,q,r) = r af r = ư³ v³ + w². Evaluate when u = 1, v = 3, and w = 4.…

A: Given function with

Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

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Q: Find the largest domain (in R²) for the function 1+ Vr+ Vỹ x² + y² f(x, y) : =

A: Given: The function f(x, y)=1+x+yx2+y2.

Q: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: The complementary function (C.F) for the (D² + 8²)y = 0 is O None O Yc = C,cos8x + C2sin16x O Yc =…

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Q: Consider F and C below. F(x, y, z) = yzexZi + e²j + xye*²k, C: r(t) = (2 + 4)i + (t² – 1)j + (t² -…

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Q: he function f(x)=3x2+2x

A: Introduction: A function is bijective if it is both injective and surjective and a function f(x) is…

Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

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Q: Consider the function f(x, y) = x²y+ y³ – 75y. f has ? v at (0, 0). f has ? at (0, –5). f has ? v at…

A: The given function is  f(x,y) = x2y+y3-75y  We have to find the value of f at  1) (0,0)  2) (0,-5)…