Consider the rormal line to the surface z= z + y? (parabokoid) at the point P(1,1, 2) Find the point where the line intersects the surface a second time C.

Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

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Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x + 11y and the plane y = 1.…

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Q: Find normal line (parametric form) to the surface x^2 − 4y^2 + z^2 + y = 27 at the point (5, 1, −3

A: This question is about application of derivative

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

A: We have to classify all the critical points for the surface…

Q: Find parametric equations for the normal line to the surface z= 3x2 + 10y2 at the point (2, 1, 22).…

A: Given the equation of surface z=3x2+10y2

Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: Consider the surfaces  z = x^2 +y^2   and z+ 2x+ 2y = 0 Find the projection of the curve on…

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Q: 14) Find the points on the surface xy- z2 = 1 that are closed to the origin. %3D

A: To find the point on the below surface that is closed to the origin. xy−z2=1

Q: Determine the projection of the following surface on the xy plane. (xy trace) 4z-목 + =0

A: here first solve the given surface and then we trace it

Q: 9) Find a point on the surface z = 8- 3x2 - 2y2 at which the tangent plane is perpendicular to the…

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: Classify the surface: 1 – x = 3y + 4z?

A: Given :  The surface 1 - x = 3y2 + 4z2.   To classify the given surface.

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

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: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z² 24 and the paraboloid…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: Find the area of the part of the surface z = x² + 2y that lies above the triangle with vertices…

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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: 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 parametric equations for the normal line to the surface x2 + 9xyz + y² = 11z2 at the point (1,…

A: Given:- x2+9xyz+y2 =11z2  To find:- Equation of normal line to the given surface at point (1,1,1)

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: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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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: 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 equation of the tangent plane to the surface z = In (2x + y) at the point (-1, 3, 0) . O x…

A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…

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 areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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Q: The equation of the tangent plane to the surface x2 at the point (-2, 1, 3) is Select one: +2y z-3…

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Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

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Q: Find all points on the surface xy - z2 = 1 which are closest to that origin. Let x,y,z be the…

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Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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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: Show that the surfaces x2 + 2y2 + 3z2 = 3,   x2 + y2 + z2 + 6x − 10y + 14 = 0, are tangent to each…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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: 4. Determine all points on the surface x² + 2y² + 3z² + 2xy + 2yz = 1 in which the tangent plane of…

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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

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

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Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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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: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

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: Evaluate the area of the surface generated by revolving the curve y = 2/a, from x = 0 to x = 3. y -…

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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: 13. Find all points on the surface at which the tangent plane is horizontal. 3,,2 (a) z = x°y ² (b)…

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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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