6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q 2|(xdx + ydy) along the semicircle with the line segment PQ as its diameter P

Q: (a) Let F = 4x27 + y} - (z – 1)k. Compute I7. dA where S is a square of side 5 units centered at…

A: Given that, the vector is F→=4x2i→+yj→-z-1k→. Determine the value of ∫SF→·dA→.…

Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: 1. Find Sp(r+2y)dA, where D is the region bounded by the parabolas y = r2, and y=1+2

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

Q: Find the average squared distance between the origin and the points on the paraboloid z = 4 – x² –…

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Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: 39. Find all points on the portion of the plane x+y+z= 5 in the first octant at which f(x, y, z) =…

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Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x²…

A: (3)Let (x,y,z) lies on parabolaThe distance d=x-32+y2+z2such that z=x2+4y2Lagrabge multiplier…

Q: The numerical value of 34 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: Find the positively oriented simple closed curve C for which the value of the line integral C(y^3…

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Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x?…

A: Given,                               z=x2+4y2and the point (3, 0, 0).

Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

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Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

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Q: 5. Find areas of the surfaces generated by revolving the curves about the indicated axes x =t+V2…

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Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: 2. Let f: R? → R be the function which satisfies for all (x, y) € R² that f (x, y) = xy. Use the…

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Q: 3. Let R be the region below bounded by the parabola y = 4x² and the lines 3x - 2y +3=0 and y = = 0.…

A: Follow the procedure given below.

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

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Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

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Q: 59. Find all points on the portion of the plane x+y+z35 in the first octant at which f(x, y, z) = xy…

A: We have to find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y,…

Q: Given (1 + y³)y' = x². (i) Determine a region of the xy-plane for which the given differentia…

A: Explanation of the solution is given below...

Q: 6. C is the curve of intersection of the plane 4x + 5y+ z = 0 with the cylinder x2 + y? = 4 directed…

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Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², -1s×<1 about the x-axis is

A: As per the company's guidelines, we are supposed to solve first question for you,  kindly repost the…

Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

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Q: 2 Find the points on the curve ax+ 2bxy + ay = c,ay = c, 0<a<b<c,whose distance from the origin is…

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Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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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: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

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Q: A/Find the distance between the line 2x + 3y = 5 and the point(-1,0). ( B/Find by integrating along…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

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Q: (b) Let F = (-yx², xy²). Let D be the annulus 1 < a2 + y² < 4, and let C be its boundary. Evaluate

A: Value of the given integral is

Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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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: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid 2= z +…

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Q: Find the points on the surface z²2=xy+1 that are closest to the origin using LaGrange multipliers

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Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

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