1. Computer° (x2 y222)1/2 dV, where E {(r, y, z) 0, y < 0, z > 0, 4 < 12 + y2 z2 < 16) E

Q: Continuity for Three VariablesAt what points (x, y, z) in space are the functions in Exercises 35–40…

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Q: 3. Let p= (1,2,-1) and h= (0.1,0.2,-0.1). For each of the differential 1-form w: R³ → C (R³, R)…

A: Please find the solution in next step

Q: Suppose w = In(x² + y² + z²) , x = ue³" sin(9v) , y = ue3" cos(9v), and z = ued". %3D Compute dw/du…

A: If w is a function of three variables, such that w(x,y,z) and x, y and z are further function of u…

Q: Let y = y(x) and sin(y a) + In(æ + 2y) = 3. Which of the following is TRUE? 1+2 dz а. dy y? (2yva +…

A: Topic:- derivatives

Q: The general solution for D. E. e'y- -= 0 is %3D 7-ry Uy = e - In (Imlxt+c 1-y+1 y = e- In y = x + In…

A: given differential equation is first order differential equation. By using suitable substitution we…

Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

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Q: 1) Evaluate the line integral Fdr where F(x, y, =) = (x+3y, 2y +z, xy) and y: line segment from…

A: Here, F→(x,y,z)=x+3y,2y+z,xy and γ: line segment from (2,1,3) to (3,3,5) We need to evaluate ∫γF→dr→

Q: 16. Integrate f(x, y, z) = x + Vy – z² over the path from (0, 0, 0) to (1, 1, 1) (see accompanying…

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Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: In Exercises 13–24, draw a dependency diagram and write a Chain Rule formula for each derivative.

A: Since, you have asked multiple questions, we will solve the first three for you. If you want any…

Q: 9. If o = F(x, z) dy + G(x, y)dz is a (differentiable) 1- form on R', what can F and G be so that…

A: GIven, ω=F(x,z)dy+G(x,y)dz ⇒dω=∂F∂xdx∧dy+∂G∂xdx∧dz+∂G∂y-∂F∂zdy∧dz Required dω=zdx∧dy+y dx∧dz on…

Q: Compute for the nonhomogeneous linear DE. d²s ds + dt2 s = 0, dt ds = 0, t = 0 a. 4t + 2cost %3D dt…

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Q: Let f(x, y, z) = x² sin y + y e², where x = t + 3,y = net-1 and z In 2t. %3D df at t 1 is: dt %3D…

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Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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Q: S/2,/2 e#" (ysin(z)dr + æsin(z)dy + cos(z)dz) J0,0, integrali altında tanımlanmış olan vektör alanın…

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Q: Consider the differential dz 2.ry da + (x² + 2y) dy. (11.39) %3D Evaluate the integral S2 dz along…

A: The integral, ∫(x1,y1)x2,y2dz=∫(x1,y1)x2,y22xydx+(x2+2y)dy∫(x1,y1)x2,y2dz=∫(x1,y1)x2,y2Mdx+NdyWhere,…

Q: Find the bounded solution of âyở y x> 0, t>0 where y (0, t) = 1, y (x, 0) = 0.

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Q: Let z = f(x, y) and x = 0(1), y = y(1) where f, o, y are assumed differentiable. Prove dz dz dx dz…

A: Given: z=f(x,y) and x=ϕ(t), y=ψ(t) where f,ϕ,ψ are assumed differentiable. Since f is differentiable…

Q: f(x.y)= are ) = arccos( x² +y² – 3 )+In(x²+y² –3) fonksiyonunun tanım kümesi aşağıdakilerden…

A: Given function is fx,y=arccosx2+y2-3+lnx2+y2-3. We know that the range of the cosine function is…

Q: 1. Evaluate the line integral f(z, y) ds where f(x, y) = Vx+ 2y and C is the straight-line segment…

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Q: Evaluate SSS 10e(=²+y²+z*)"² dV_over B where B = {(x, Y, z) : x² + y² + z² < 1}. Take T = 3. Türkçe:…

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Q: 4y" + 24y' + 27y = 0 @y(Tt) = 1, y'(Tt) = 0* O y(x) = 6 [e^(3(t-T!)] cos(t/2) - e^(3(t-T1) sin(t/2)…

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Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

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Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

A: My=Nx means F is conservative vector field

Q: a) If u=(x,7), where x = 0(1) and y=p(1), then that %3D prove du du dr ди dy dt Əx dt ây dt If…

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Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: dz Let z=e"In(xy), determine dx et (1+xin(xy)) dz A %3D дх az (1+xyln(xy)) %3D дх y (1+yln(xy)) %3D…

A: Explanation of the answer is as follows

Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

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Q: 2. Let z = g(x, y) = e" cos y + y In(x – 1). %D Use local linear approximation to estimate g(1.99,…

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Q: 4. Evaluate ||| x y dV , where E is bounded by the parabolic cylinders y = x², y' = x and the planes…

A: The region E is bounded by the parabolic cylinders y = x2, x = y2 and the planes z = 0 and z = x +…

Q: Evaluate SSS7elz²+y?12)"" dV over B where B= {(x, y, z) : z² + y² + z² < 1}. Take = 3. Türkçe: B =…

A: Here we will find out the required value.

Q: If w = x²y - y²z³,x = rCost,y = rSint, dw z = re' , (r = 2)and(t = 0)then dt

A: Given equations - w = x2y-y2z3       ...............(1)x = rcost        ............(2)y = rsint…

Q: . Given: WZ 1 ZY; WX 1 XY; WX = YZ Prove: Wz || XY Y W

A: Since, we have been given that WZ ⊥ ZY , WX ⊥ XY and WX ≅ XYOur Aim is to prove that WZ  ∥ XY

Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

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Q: Consider p(x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z)= F₂(x, y, z)i + F₂(x, y,…

A: Let F→=f1, f2, f3. The gradient of the scalar field: g is defined as: ∇g=∂g∂x i^+∂g∂yj^+∂g∂zk^. The…

Q: Find the total differential for the function w = 13z ysin x. dw = 13z ysin xdx-13z sin xdy-26z ysin…

A: Consider the function: Let,  w=13z3ysinx=fx,y,z The total differential of the function is given by…

Q: Let f(x, y,z) = x? sin y+y e, where x = t+3,y = net-1 and z = In 2t. %3D at t = 1 is: df dt О 12п O…

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Q: O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the…

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Q: 3 Find the bounded Solution of : = xt メ>。,t>。 >y(メノ) where y cx, o) = %3D and y co,t) = 0 . Ansi] y=…

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Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: Let W = F(x , y, z) = xy + yz + xz , where x(t) = 3 + sin(2t -4) , y(t) = t 2 and z(t) = 3 - t. Find…

A: Given that :    W= f(x,y,z) = xy+yz+xz.  Here we use chain rule to find dw/dt  at t= 2.   Here i…

Q: 4.(i) Consider the function z= f (x,y) and the total differential of it, dz given by dz = fx dx + fy…

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Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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