3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below the plane z = -1.

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

A: Horizontal tangent plane

Q: Evaluate the surface SS₂ xz ds S is the part of the 2x+2y+z=4 that li- the first octant.

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Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

A:

Q: r2 0, Is es 2

A: We draw the graph of following function.

Q: 39. Find the surface area of the portion of the hyperbolic paraboloid r(u, v) = (u+ v) i + (u – v)…

A:

Q: 5. Use polar coordinates to find the volume of the solid enclosed by the hyper- boloid –r² – y² + z²…

A: To obtain the limits of integration for z, rewrite the equation -x2-y2+z2=1, and find z.…

Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

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

A:

Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: The value of . (x² +y²) dS, where S is the surface of the paraboloid z = 2- (x² + y2 ) above the x-y…

A:

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

A:

Q: Find the approximate area of ​​the part of the plane x=z that is between the planes y = 0 and y = 6…

A: As per the question we have to calculate the area of the plane surface x = z bounded by the planes y…

Q: (b) Find a parameterization, in spherical coordiantes, for the ellipsoid 4x2 + 9y2 + 2²/4 = 1 that…

A:

Q: By transforming into spherical polar coordinates, evaluate JJ) 1-x². ff - (- dxdydz , taken…

A:

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 O x - y -…

A:

Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

Q: 2. With the help of polar coordinates and the following formula, find the surface area of the…

A:

Q: (4) Use Stokes' Theorem to evaluate 11. Vx (yz, xz, xy) dS where S is the surface S that is the part…

A:

Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

A:

Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x + 2y and the plane z = 8.…

A: Dear student, you didn't mention which question is to be solved so according to Bartleby guidelines,…

Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

A:

Q: Evaluate the surface integral: S Ss a?y ds Where S is the surface of the paraboloid z = 4- x2 – y²…

A:

Q: 2. Use polar coordinates to find the volume of the solid under the paraboloid z = x² + y² and above…

A: Let's find volume of solid by using polar coordinates.

Q: 9. Find the surface area of the part of the paraboloid a = 2 – 2? – y? that lies inside the surface…

A:

Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: Given a surface 2xy - In (5z - 2) = -10, where z = f(x,y). Find Zx at y = -10, z = 1. Leave your…

A: Partial differentiation

Q: Find the area of the surface of the part of the plane 3x + 2y + z = 6 that lies in the first octant.

A:

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

A:

Q: 28. Show that the ellipsoid 2x² + 3y² + z² = 9 and the sphere %3D x? + y? + z? - 6x – 8y – 8z + 24 =…

A:

Q: What is the equation of the plane to the surface z = e3Y sin(3x) +2 at the point P,0, 3) O x- y + ez…

A:

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

A:

Q: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

A: We will find out the required value.

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

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Q: For the surface a?+ - z = 1, a curve in a form of a parabola can be formed bi passing through a…

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Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: Given a surface 3xy - In (3z - 2) = -5, where z = f(x,y). Find zx at y = 3, z = 1. Leave your answer…

A: This question is based on Partial differentiation of function

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

Q: Given a surface 5xy - In (2z - 5) = -1, where z = f(x,y). Find zx at %3D = -9, z = 1. Leave your…

A:

Q: 3) Find the surface area of the portion of the paraboloid z = x2 + y2 below the plane z = 1. %3D

A:

Q: a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r…

A:

Q: Given the surface z = In(-2x² + 5y² – xy). Find the equation of the tangent plane and the parametric…

A: Surface given z=ln(-2x2+5y2-xy) Point P4,3,0

Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: Find, by using polar coordinates in R2, the volume of the region bounded by the paraboloid z = 20 –…

A:

Q: 2)use the polar coordinates to evaluate the double integral A) | x2 + y2 dA , R is the disk x2 + y?…

A:

Q: 4. Consider the equation 16y" - 4 + 2² = 16. By first deseribing all of its traces, sketch the…

A: Given,  The equation, 16y2 -4x2 + z2 = 16

Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…

A:

Q: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.