Integrate ƒ(x, y) = 1/ (1 + x2 + y2 )2 over a. Triangular region The triangle with vertices (0, 0), (1, 0), and (1, sqrt(3)). b. First quadrant The first quadrant of the xy-plane.

Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: Using Lagrange multiplier, find the minimum value of f(x,y) = 3x +ly on the circle x2 + y2 = 1. Give…

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Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

A: 25.   Given that:   The plane y+z=2 and the cylinder x=4-y^2. The region in the first octant bounded…

Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (5,2,0) on the…

A: The equation of the surface is -cosπx+2x2y+4exz+4yz=105. The function is fx, y,…

Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…

A: Here, the surface is in the first octant. Therefore, the integration is

Q: * = Vy +5,

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

Q: The region bounded by the curves y = r² and y = x³ is rotated around a. the z-axis; b. the y-axis;…

A: the region bounded by the curves y=x2 and y=x3 is rotated around  a) the x-axis b) the y-axis c) the…

Q: Solve the problem. Find the equation for the tangent plane to the surface z=2x2+10y2 at the point…

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

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers…

A: The angle between two planes is equal to the angle between their normals.

Q: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 4 − x2, y = 0,…

A: Calculations: Point of intersection are given by: 4-x2 = 0 =>x2 = 4 =>x = -2, +2 Since, x…

Q: Find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis

A: We have to find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis.

Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

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

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: The plane z =0 separates region 1 (z 0), which is a dielectric material with ɛ, = 4, from region 2…

A: The complete solutions are given below

Q: Find the distance from the point (2, 0, 0) to the plane x + 2y + 2z = 0.

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

Q: Find the average height of the paraboloid z = x + y over the square 0sxs2,0sys2. The average height…

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Q: Find the area of the surfaces The portion of the plane y + z = 4 that lies above the region cutfrom…

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Q: Find the area of the surface. The part of the surface y = 4x + z2 that lies between the planes x =…

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Q: Find the area of the surface generated by revolving the curve y = / 2x - x , 0.75<x<1.75, about the…

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Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: 9ху. Use hyperbolic functions to parametrize the intersection of the surfaces x - y = 49 and z =

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Q: Find a harmonic function ¢(x, y) in the right-half plane x>-1 such that on the boundary (-1, y) = 0,…

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Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

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Q: Find the area of the upper portion of the cylinder x2 + z2 = 1 that lies between the planes x = ±1/2…

A: Find the area of the upper portion of the cylinder x2 + z2 = 1 thatlies between the planes x = ±1/2…

Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: Find the area of the surface. The portion of the plane y + z = 4 that lies above the region cut from…

A: Given:

Q: The base of a solid is bounded by y= x² and y= 4. All parallel cross – sections are squares…

A: Please rate

Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

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Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the…

A: Please see the attachment

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 area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: :y² + z² — ² by first sketching at least three cross sections in each of the 4. Graph the surface 1…

A: A quadric surface is a graph of an equation in the three variables x, y and z in a three dimensional…

Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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Q: area of the portion of the cylindrical surface y = 4 − x2 in the first octant that is between the…

A: Given: The cylindrical surface is, y=4-x2 ........(1) And the xy-plane is, x2+2x+y-z =4

Q: The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine…

A: Given curve, y=64x-4x3 The shaded region is shown as: Formula for the centroid x, y in a region is…

Q: nal projection onto the plane x + 2y+3z = 0 %3D

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Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Find parametric equations of the normal line to x2 the surface z = 4 + y? at the point (2, 3, 10)

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Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

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Q: A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum…

A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F.  To find :-…

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: Given that, the cone is generated by revolving the line segment  y = 53x,  0≤x≤4, about x-axis.