1. f(x, y) = 192x³ + y² – 4xy2 on the triangle with vertices (0,0), (4,2) and – 2,2). %3D

Q: Compute the triple integral and please show work

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Q: Find the maximum and minimum values of the function f(x, y) = 3y² + 2x² – 6y %3D in the region where…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: I need help finding the absolute maximum and minimum values of f on the set D.

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Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

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Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: 2. Find the absolute maximum and minimum values of f(x, y) = 4x+6y-(r²+y?) on the rectangular region…

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Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and (0,0,4)

A: x varies from 0 to 1&amp; y varies from 0 to 2 and z varies from 0 to 4.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

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Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

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Q: f(x, y) = xy over the triangular region with vertices (0, 0), (8, 0), and (0, 6) O 12 2 96 O 16

A: Solve

Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

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Q: D be the region that consists of points (x, y) such that x² + (y - 3)² ≤9. Then, (x² + y²) dA equals…

A: see my solution

Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

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Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

A: We have to find x

Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

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Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus