z = 0 and z= 2. Compute JJ FdS, where S is the surface of the cube bounded by the planes x = ±1, y = ±1, z = ±1, if (a) F = xi (b) F = xi+yj (c) F= xi+yj + zk (d) F = x² + y²j + z²k (e) F = yi (f) F = zi (g) F = z²i

Q: SUppose F(x) = dt. Find the formda 13 F (x ³) expressed using an integral. ? F (x* )= ]

A:

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

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A: We have to do implicit differentiation.

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A: Determine the x- coordinate of the point for which the tangent is horizontal to the function

Q: Q1) Find the canonical form of these question : a) f(x.y,z) =F=x' y' z+x y° z" +x y z b) f(x.y.z)…

A: We are given: f(x,y,z)=F=x'y''z+xy''z''+xyz We are given the standard Form. F=x'y''z+xy''z''+xyz…

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A:

Q: P(a,1, 0) す(い)。 レ 1-人2 2) 3. Find divergence at

A:

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: 6) Show that (2xy, 2yz + x², y²) is conservative.

A:

Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: The maximum error for F=yx2+y+y2 are |(2xy)Ax| +|(2y+1 + x²)Ayl |(2x + y)Ax| + |(2y + x)Ayl x|Ax|…

A: Given function is, F=yx2+y+y2

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].