The solid lies between planes perpendicular to the x-axis at x = 0 and x = 6. The cross-sections between these planes are squares whose bases run from the x-axis up to the curve x2 + y½ = V6.

Q: Find the area of the surface generated when the given curve is revolved about the given axis.Y=…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: Y is the midpoint of XZ and V is the midpoint of WZ. If VY = 32, what is WX? WX Submit

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

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Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

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Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

Q: Find the surface area of the solid that is obtained by rotating the graph of y = f (x) about the…

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Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

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Q: Find the vollumes oF the solid that results when the r egion enclosed by the curves y= x, x = y is…

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Q: Find the points on the surface x2 - zy = 4 closest to the origin.

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Q: Find the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0&lt;=x&lt;=…

A: To Determine: Find the area of one side of the “wall” standing orthogonally on the curve…

Q: The plane x+ y = 1 intersects the paraboloid z = in a parabola. Parametrize the whole parabola using…

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Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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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…

A: Compute the partial derivative as follows.

Q: The area of the surface obtained by rotating the curve y = V25–x2, -4 < x s 4 about the x-axis is

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +5…

A: Surface area of the bounded region along x axis

Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: 3. z = (c

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Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 4x, x = 1 and x =…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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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: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +…

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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: Find the point(s) on the surface z = 3x2 + 2y2 − 3x + 4y − 5, at which the tangent plane is…

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Q: The surface of a hill above the xy-plane is described implicitly by 3x² + y² + (z + 1)² = 2, z ≥ 0.…

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Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

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Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

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Q: Find the area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

Q: The area of the surface obtained by rotating the curve y = V4-x², -2 s xs 2 about the x-axis is

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Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the…

A: We have to find the point closest to the origin on the curve of the intersection of the plane…

Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: Find the surface area of the object obtained by rotating x = Vy-6 2sys3 about the y-axis.

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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: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

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

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Q: Find the exact area of the surface obtained by rotating the curve abo = V7 - x, 1<x< 7

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

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