Sketch the surface z = f(x,y). flx.y) = - +y? OA. O B. OC. OD. y

Q: Find the plane tangent to the surface z=x x+ y° at the point (3,4,25). a. 6x+8y-z=25 O b. 6x-8y-z=25…

A: As we know that; The equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 And The normal vector at…

Q: Evaluate the surface integral. || x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: ∫∫sx2yzdS where S is the part of the plane z=1+2x+3y that lies above the rectangle…

Q: Calculate F · dS where F = (e* sin cos y, yz?) y, et and S is the surface of the box bounded by the…

A: By using the divergence theorem, we can make equality between the surface integral of a function and…

Q: Find the area of the surface generated by revolving the curve about the (a) x-axis and (b) y-axis.…

A: Explanation and solution is given below....

Q: Compute dS where F = (x, Y, z) and S is the surface of the cone z2 = x² + y² for 0 < z < 4 plus its…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: Sketch the surface z = f(x.y). f(x.y) = - /x² +y?

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Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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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 tangent plane to the surface z = cos(3ry) + z' + 2y at the point (1,0). (z = cos(3ry)+z'+…

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Q: Evaluate [F•ds where F = xi – yj+(x+ y+z)k and C is the boundary of the surface C z =1,0<x,y <1.

A: The solution are next step

Q: Evaluate the surface integral. /| x*yz ds, s is the part of the plane z=1+ 2x + 3y that lies above…

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Q: Consider the surface S(u, v) = -dS.

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Q: The slope of the tangent line to the curve of intersection of the plane r = zo and the surface z=…

A: In the given problem we have to find the slope of the tangent line to the curve of intersection of…

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Let f(x, y) = x² – y?. Find (b) The tangent plane to the surface given by f at the point (0, – 1).

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Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: (b) Find the point that makes the tangent plane to the surface z = x² – xy + y? – 2x + 4y…

A: Find the partial derivatives with respect to x and y and set equal to zero. Solve for x in the…

Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

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Q: At which of the points below is the tangent plane to the surface z - 2y + z?+ yz = 2 vertical?…

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Q: Find the point on the surface f(x,y)=x2+y²+xy+21x+7y at which the tangent plane is horizontal.

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Q: Evaluate the surface integral. || x²yz dS, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: The surface integral, ∫∫Sx2yz dS, S is the part of the plane z=1+2x+3y that lies above the…

Q: Which type of surface does the curve x=t2, y = tsin(t), z=tcos(t) lie on?

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Q: Sketch the surface z = f(x,y). f(x.y) = 4x² + 4y² + 2 OC. OD.

A: Given function is fx,y=4x2+4y2+2. We have to sketch the surface of fx,y=4x2+4y2+2.

Q: Find the unit normal to the surface z=2+2z^2-3y^3 at the point (1,-1,7), pointing down with respect…

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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 equation of the tangent plane for the surface z = xy at the point (-1,2,-2) O z=x-2y+2…

A: The equation of tangent plane for the surface z =f(x,y ) at point (m,n,f(m,n)) is given as:

Q: Find the plane tangent to the surface z = x cos y - yex at (0, 0, 0).

A: Consider the following function: z=fx,y=xcosy-yex Differentiate function fx,y with respect to x:…

Q: Find the area of the surface defined by z = xy and x2 + y2 < 7.

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Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: Find the point on the surface f(x,y)=x+y2+xy-24x+2y at which the tangent plane is horizontal.

A: We have to find the points for horizontal tangent plane.     According to our guidelines , We can…

Q: Let F(r, y, z) = 2x² + 14y? + 722. Find the equation to the tangent plane to the level of surface…

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Q: Find the point on the surface f(x,y)=x²+y²+xy+24x+13y at which the tangent plane is horizontal.

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: If the tangent plane to the surface z = +y is parallel to the plane r+ 2y-z 0 at the point (1, a,…

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Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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Q: Calculate , f(x, y, z) dS For Part of the surface x = z', where 0 < x, y < 13-2; f(x, y, z) = Is…

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Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: Sketch the surface z = f(x,y). f(x.y) = 4x2 + 4y2 + 2 O A. OB. OC. OD. N

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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: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 < x < 3, 0 < y < 1.

A: Given surface is z=f(x,y)=1+2x+3y+4y2 where f(x,y)=1+2x+3y+4y2 Differentiate f(x,y) partially with…

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: Consider the surface defined by f (, y) = ln(5y – 7x). Find the equation of the tangent plane to…

A: Given: fx,y=ln5y-7x We have to find equation of tangent plane to fx,y at the point 2,3.

Q: Show that the tangent plane to the surface x 2 a 2 + y 2 b 2 = cz at the point P(x0, y0, z0) is…

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Q: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

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: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.