Classify all critical points for the surface flaiy)= 2x-y-2xy.

Q: Find the points on the surface xy + yz + zx - x - z2 = 0 where the tangent plane is parallel to the…

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Q: Use a computer algebra system to graph the surface and locate any relative extrema and saddle…

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Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: Find the uolume of the soild olbtained by the grophs bounded by potaling the begion Y = x² +1 and Y…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 1 <x < 1 y =…

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Q: Find the points on the surface y = 4 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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Q: Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: How would you evaluate [[ F-dS, where S is the surface with param etrization G(4, v) with domain D?

A: We need to demonstrate the method of evaluating the surface integral. ∬SF.dS Where, parametrisation…

Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = 2 + 3y2, 1 <…

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Q: Find a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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Q: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

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Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…

A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

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Q: 4. Find the area of the surface obtained by rotating the curve x²/3 + y>/3 = 1, 0 <y<1 about y-axis.

A: If the curve defined by the parametric equations x=x(t), y=y(t)  with a≤t≤b , is rotated about the…

Q: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

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Q: Find the area of the surface obtained by rotating the curve y = x², 0 < x< 1, about the y axis.

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Q: Find a parametrization of the curve. The intersection of the surfaces z = x^2 − y^2 and z = x^2 + xy…

A: Given : The surfaces z = x2 - y2 and z = x2 + xy - 1.   To find the parameterization of the curve.

Q: Find the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: 18. z = 4 – x2 – y², 0<z< 3; f (x, y, z) = x² / (4 – 2) - -

A: Use polar coordinates to solve the integral

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x 1 < x< 1…

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Q: Calculate the points of intersection of the curves x² = 4y and bn=) = y 29vaus at newed biloa gris 1…

A: Centroid: The centroid or centre of mass of a region bounded by the curves is the point where the…

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

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Q: Classify the surface: 1– x = 3y² + 4z² O Elliptic paraboloid O sphere O Ellipsoid O Plane O cone

A: In this question we have to classify the surface.

Q: Find the exact area of the surface obtained by rotating the curve x = 1/3y3, 0 &lt;= y &lt;= 1,…

A: For rotation about y-axis, the surface area of the curve is given by

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…

A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…

Q: 2. Calculate the centroid of the thin plate R which bounded by r = 1, y = 0 and, 2² + y² = 4.

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Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: the tangent plane of the surface [ z=x^5+e^(xy)cosyx] at the point (1,0) O z=5x-y-3 O z=5x+y-3 O…

A: Above question is solved.

Q: Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…

A: This is parameterisation of curve problem

Q: x = 1+ 2y2, 1< x < 2 about the x-axis.

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Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (y2 + 2)3/2, 2 <…

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Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density δ =…

A: Given: y=2x and y=4 Thus the region bounded by the y-axis and the line y=2x and y=4 is shown as…

Q: 2. Find the area of the surface obtained by rotating the curve: y = Vx +1,1<x<5 about the Х-ахis

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