(A) Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder x² + y² = ax

Q: Find the area of the surface generated by revolving the semicircle y = √1 − x about the x-axis over…

A: Given that, y=1-x. dydx=121-x-12·-1=-121-x 1+dydx2=1+-121-x2=1+141-x=1+14-4x=4-4x+14-4x=5-4x4-4x

Q: Find the surface area of the portion of the half ball with a radius a which cuts off by the cylinder…

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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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 volume of the shaped body bounded by the z = 3x2 + 3y2 and          z = 4 - x2 - y2…

A: We have to Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and        z = 4 - x2 -…

Q: Find the point on the surface z = xy + 1 nearest the origin.

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

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Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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Q: 2. Find the area of surface that is generated by revolving the portion of the curve x = V16 – y , 0…

A: Given, x= √(16-y) Therefore, f(y)= √(16-y) Differentiating the above equation with respect to y we…

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 portion of the cylindrical surface y = 4 - x2 in the first octant that is…

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Q: 6. Find the area of the surface generated by revolving the curve y = x² + 2 from x = 1 to x = 2…

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Q: 5.Find the area of the surface generated by revolving the given curve about the y-axis. x = /9- y, -…

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Q: 3. Find the area of the surface generated by revolving the curve = 2/1- y (-1 < y < 0) X about the…

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Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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Q: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside the…

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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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: The curve y = sqrt(x2 + 1), 0&lt;=x&lt;=sqrt(2), which is part of the upper branch of the hyperbola…

A: Find dy/dx from the given curve using power rule and chain rule.

Q: 1.a)Find the area of the surface generated by revolving the curve y=√(121-x^2), −1 ≤ x ≤ 1 about the…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: The figure shows the surface created when the cylinder y2 + z2 =1 intersects the cylinder x2 + z2 =…

A: It is given that, the cylinder y2 + z2 =1............... (1) intersects the cylinder x2 + z2 = 1…

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: The figure shows the surface created when the cylinder y2+z2 = I intersectsthe cylinder x2+z2=1 Find…

A: Given : surface S (say) is created when the cylinder y2+z2=1 intersects the cylinder x2+z2=1 To find…

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 area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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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: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

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: Find the area of the surface formed by revolving the graph of y = Vx + 2 on the interval [1,8] about…

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Q: Find the points on surface z^2=xy+4 closest to origin.

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

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Q: 2. Find the area of the surface obtained by revolving the curve g(x) = Vx +1 on the interval 0 < x <…

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Q: Find the surface area of revolution about the x-axis of y 7x + 7 over the interval 0 < a < 3

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Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: Find the area of the surface obtained by rotating the curve y =÷x/2 – x³/2 for 0 < x < around the…

A: We find dy/dx using power rule

Q: 5. Find the volume generated by the equation x2 +y² – 4x - 6y –- 12 = 0 if it is rotated about the…

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Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: 4. Find the area of the surface generated by revolving the given curve about the -axis. y = 7x,0 <…

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Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: Y = e-5x x > 0

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

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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