270. f(x, y, z) = 1 √x² + y² + z², B = {(x, y, z) |x² + y² + z² ≤ 9, y ≥ 0, z ≥ 0} N 3 2 0 0 1 y 2 3-3 0 X 3

Q: Evaluate (x-5y+z)ds, where S - Sz 10 x, 0 ≤x≤ 10, 0y ≤ 10.

A: Step 1: Step 2:

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: The domain of F(x, y) =x*y+ x*+ = 1 D =R²- {(0, -)} A O D=R BO D=R? .C O D=R-{}

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Q: ame: Date: 1. fx]=x +2x -X-2 2. x)=x-2x 8 Rel. Max Rel. Min: Rol. Mox Rel Min: Abs. Mox. Abs. Min.…

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Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: 2. - q + (q Ap) ~q (q p) T F F T F F 2

A: We have to find the truth table for given statement.

Q: 3. x = 1-5t and y -t+ 3 for 2 < t<6 %3D y (x,y) Domain:

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Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: Consider the LP problem below: Max P= 12x + 10y Subject to: 4x+3y =0 Which point is the…

A: Given: To find - Intersection point of,

Q: Evaluate |(a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b₁ e²a+b; y = a² + t² + 1 да

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Q: Given the vector field (yz, xz, xy) find a potential for this field.

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Q: P = (x, y) = x + 4y ≤ 13 3x + y ≤ 6 x ≥ 0, y ≥ 0.

A: Let us first find the feasible region.

Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: 6). Solve xdy- yk -0 x +y* xdx + ydy +-

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Q: 5) y = V V+ V? + Væ

A: The function: y=x+x2+x

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: It is the case that (x4 – y4)", where A=7 and n > 0 is a parameter, simplifies to x" – y". Please,…

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Q: I= || elx²+y?)² dA, where R R={(x,v)E R² | x²+y²s 25, x2 0}, then 25 si 25 4 75 ne625 <IS 25ne625 4…

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Q: 21. Let V1 = 1 0 -1 V2 H " V3 = 0 {V1, V2, V3} span R4? Why or why not? 1 0 0 . Does

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Q: c. P((X,Y) ¤ B3) where B3 = {(x, y) = R² : |x| ≤ 1, |y| ≤ 1}. d. P((X,Y) € B4) where B4 = {(x, y) =…

A: Given R={(x,y)Area of R=c.       Area of ,therefore     P((X,Y))==1d.   Area of ,therefore   P((X,Y)…

Q: aff (² Find (3x + 2y)dA where D = {(x, y) | x² + y² ≤ 25, x ≥ 0}

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Q: dx +x3 4cos2y dy

A: dxdy+x=4cos2y

Q: 46) y=2cesh+va -4 (ans.:

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A: Solution: