Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct to two decimal places.

Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

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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: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

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Q: Evaluate (x + 2y) dA, where R is the region bounded by the parabolas y = 2x² and y = 1 + r?.

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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: Q6/ Find the moment of inertia and radius of gyration about the x-axis of a thin plate bounded by…

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

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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: Find the equation of the tangent plane to the surface z = e17 In(1y) at the point (-3, 1,0). Note:…

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Q: (c) : Find the area of surface generated by revolving the curve about x- xis y = Vx - x3/2, 1< x <…

A: c) Given y=x-13x32, 1≤x≤3 y=f(x) is a continuous function in the interval [a,b] S=2π∫aby1+y'2dx…

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: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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

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Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: Find the absolute maximum value of the function f(x, y) = 3x² + 2y² – 4y+1 | on the disk which has…

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Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: first orde pde 4yzp+q+2y=0 and passes through the ellipse

A: We have to find out the equation which satisfy the given PDE and passes through the given curves.…

Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: Find a generating curve and the axis of revolution for the surface                             x2 +…

A: Find a generating curve and the axis of revolution for the surface   x2+3y2+z2 =9 If the equation of…

Q: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

Q: Find a parameterization for the hyperbolic paraboloid z = z – y².

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Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

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: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

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Q: y 1 X 1 2.

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Q: 8) Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y?…

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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: Find the average height of the paraboloid z = x2 + y2 over the square 0&lt;= x &lt;= 2, 0…

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Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

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: H.W 1. Find the centre of mass of a thin plate of density & = 3 bounded by the lines x 0, y = x, and…

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Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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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: Use numerical integration with Ax = 1.0 m to locate the centroid of the surface generated by…

A: Given That : y=3x216 and ∆x=1.0 m To find : locate the centroid of the surface generated by…

Q: Find the minimum of f(x,y) = 4x + 5y on the ellipsoid 9x2 + ly2 = 7. Leave your answer correct to…

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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: Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant…

A: Consider the given curve.

Q: Sketch the curve y2 = x(x-4)2 and find the volume of the solid of revolution formed when the closed…

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Q: y. y:3x- 31 to

A: Consider the figure, which is given below

Q: *Q. ( 12 ), p. 410 : Find the area of the surface generated by revolving eУ + е-У the curve x = 0…

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Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

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Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

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Q: Graph the surface 1 = y2 + z2 –- by first sketching at least three cross sections in each of the xy…

A: We have to sketch the graph of the following surface in the 3D space: . First we have to sketch the…

Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

Q: Find the moment of inertia of the solid formec y2 = 2x and th

A: Introduction: If a solid is formed by revolving an area about the y-axis, then the moment of inertia…