[ 64–x² 64-x²-y 2x? dzdydx. Use cylindrical coordinate to evaluate La LIe4-r2 So

Q: Suppose r(t) = ⟨t, 0⟩, for a ≤ t ≤ b, is a parametric description of C; note that C is the interval…

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Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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Q: J: Use cylindrical coordinates to evaluate the integral: 16–22 16–y²–22 drdydz.

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Q: x³ +1 Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = 1+²dy into the surface area of the object…

A: Find the arc length of y=x+2, 1≤x≤7 using the differential element ds=1+dxdy2dy. For formula for…

Q: Integrate F(r)= [e2*, e²y,e²²] along the helix that cuts the z-axis at c.

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Q: 1 in 1in y 1 in 3 in 1 in X

A: Consider the diagram and divide into four regions as shown below, Now, make a chart and evaluate…

Q: Consider f(z, y) = Vzy+ 2y? ry- %3D Approximate f(2.4, 1.04) by using the tangent plane.

A: f(x,y)=xy+2y2

Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: A) || Jx2 + y2 dA , R is the disk x2 + y? < 9

A: We have to use polar coordinates here.

Q: Q.2) Evaluate x+ y ds where o is the portion of the plane 3r+2y+z 6 in the first octant.

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Q: Find the point on the surface z=x2-y2 at which the tangent plane is parallel to the plane…

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Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8 that lies inside the cylinder x?…

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Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Use Y=sin) and reductiori of order to find the generale soletion to the homogeneous differenticl…

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Q: (Q.)AUSE T.cx)-1 ad Tilx)= X, t fnd TECK) nd 万(x) (b) Find the raats of Ti(K) nd Tiw using the…

A: a) Given that, T0x=1 and T1x=x. Note that, the powers of x as function of Tnx for x2=12T0+T2 and…

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: Find of and Duf to :- f cas,z) = In (x²+zy?+32) atp(-v34) in the direction of ã=-3i-4j-12K. -314…

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Q: Let z be a complex mumber , f() b any funcion, and c be contour any then to f B(Z)dZ?

A: Let z be a complex number, f(z) be any function and c be any contour.     A contour is a type of…

Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: Given that F = (2x + y2)i + (3y – 4x)j. Verify Green's theorem for F.dr around the triangle formed…

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Q: - 2+ 7x + 4y that lies inside the cylinder Find the surface area of the part of the plane z = x² +…

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Q: Use cylindrical coordinates. Evaluate |/| 6(x3 + xy²) dv, where E is the solid in the first octant…

A: We have to evaluate the integral ∬∫E6x3+xy2dV, where E:z=4-x2-y2 in the first octant.

Q: Use cylindrical coordinates to evaluate each of the following: 1. SSL, z³dxdydz, where T: 0 <x< 1, 0…

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Q: Use Stoke's theorem to evaluate // curlF - dS where F(x, y, z) = 2y i+ 3xj + (z – x) k and S is the…

A: The given integral is∫∫CcurlF→·dSwhere F→x,y,z=2yi^+3xj^+z-xk ^and S is theportion of y=11-3x2-3z2…

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: dx dy, where D is the disk x2 + y² < 9. (x² + y?)3/2 Evaluate

A: The given integral is,

Q: Use Cartesian coordinates to evaluate JIJ y² dV D where D is the tetrahedron in the first octant…

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Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: Use Cartesian coordinates to evaluate JIJ y² dv D where D is the tetrahedron in the first octant…

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Q: V9/ Compute I ,cxyz), uhere s is the part f the plane +x that lies inside the half - cyllnder…

A: Given: The Integral is ∬SxyzdS. The surface is the part of the plane S  z=y+x that is inside the…

Q: Compute where h(s) = rs? -r. Assume r is a constant. %3D ds

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: dA, where K is the disk r + (y 2 +?

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the moment of inertia of the plane area generated by the equations y = 8x³, y = 0, and x = 1…

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

Q: Use Stokes's Theorem to evaluate F(x, y, z) = z²i+yj + zk S: z = √√16x2 - y2 6 F. dr. In this case,…

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Q: Use Stokes's Theorem to evaluate F(x, y, z) = z²i+yj + zk S: z = √4x² - y2 F. dr. In this case, C is…

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Q: 157. Calculate -x²ydx + xy? dy, where C is a circle of radius 2 centered at the origin and oriented…

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Q: i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

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Q: Use Green's Theorem to calculate (422 – 3yx)dr + (3xy+ y² + 6)dy where C is the circumference (x –…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder æ? + y² = 5, and…

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Q: Find the work done by the force field F(x,y)=5x2i−2xyj on a particle that moves once around the…

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Q: Evaluate ||| Vx² + y² + ²²&V where S lies above the cone z = Vx² +y° and between the spheres x + y…

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Q: (a) Find the point of intersection between the curv urve r(t) = (cos(at), sin(at), t²) and the…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: The r in cylindrical coordinates must be positive or zero. O True O False

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Q: x3 + axy? +1+ iv(x, y) dz |z|=1

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

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