Find the point on the surface r² – 2ry + 2y² – x +y = 0 closest to the point (1, 2, –3).

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: At what points does the curve r(t)=(t,t,14t) intersect the surface z=x2+3y2?

A: Given: rt=t,t,14t, z=x2+3y2 for finding intersection point of curve and surface we put point t,t,14t…

Q: Evaluate yze-y dS V(1+ x²)e2v + 1 where S is the surface z = xe", 0 < x < 2, 0 < y < 3.

A: Given: ∬Syze-y1+x2e2y+1dS            where Sis the surface z=xey, 0≤x≤2, 0≤y≤3.

Q: F = z i + 2x j + 3y k, and S is the part of the surface z = x + y above the rectangle 0 ≤x ≤3, 0 ≤y…

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Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

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

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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: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

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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 the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

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Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

Q: Q3/ Examine the following surface for maximum and minimum points z = 2x2 + 3xy + 4y² – 5x + 2y

A: Since you have posted multiple question according to company rule we are supposed to give solution…

Q: sketch the given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

Q: Find the equation of the surface of revolution of x = z2 about the x-axis.

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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: (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: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: Find an equation of the plane tangent to the surface z = x2 - y at the point (2, 1, 3). O A. 4x - 2y…

A: Find an equation of the plane tangent to the surface z= x2 - y2 at the point (2,1,3). Here i…

Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: Let f(x,y)=/4– 4x² – y² . Find its domain and give a rough sketch of its surface.

A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

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Q: Find the surface which intersects the surfaces of the system z(x+ y) =c(3z+1) orthogonally and…

A: To finding the surface which is intersecting given system and orthogonal to circle is given as…

Q: Evaluate ∬S(x2+y2)dS, where S is the surface z=4−x, 0≤x≤2, 0≤y≤2.

A: Given z=4-x , 0≤x≤2 ,0≤y≤2 to evaluate ∬Sx2+y2dS where S is surface

Q: Evaluate /F. .7 dS where F = (³+y²z)7+(y²+a²y)7+(2x²z+y^) k" and S is the surface of the cylinder x2…

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Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla

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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 a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: (y – 3)² - Consider the surface T with equation 4 + 22 = 1. 3

A: Curve sketching (or curve tracing) is a technique used in geometry to get a general impression of…

Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

Q: Sketch the section of the surface at y = 0. z = V4 +x² + y? 6 6 -8 -6 -4 -2 -2 -5-4-3--1, -8 -6 -4…

A: Given query is to the graph of the given expression.

Q: Integrate G(x, y, z) = x2y2 + 4 over the surface cut from the parabolic cylinder y2 + 4z = 16 by the…

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Q: Q2 Find the maXimum and minimum values of aFunction FCXS.2) = 8x+j+ 2 en the Surface x+y, z"=18 %3D

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Q: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

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Q: Find the equation of the integral surface of the PDE 2y(z- 3)p+(2x- z)q = y(2x – 3) which contains…

A: Here to finding the equation of integral surface to given partial differential equation we use the…

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

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Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: : The trace of the surface S x² Z = + 9. 4 in the plane z = 4 ||

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Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

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