Evaluate f, (2x? + 2y2) dS, where S is the portion of the cone z2 = 8x2 + 8y2 for 0szs 4V2.

Q: If KN=2x+1 and NJ=3x+5, what value of x makes point N the centroid? K, J M

A: (1).   If in the given triangle N is the centroid then the point N divides the line HL, JK and LM in…

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: Evaluate x² + y? – z dS where S is the part of the cone z? = x² + y² that lies between the planes Z…

A: To evaluate :  Where , S is the part of the cone , that lies between the plane   and .…

Q: Find the length of the curve. r(t) = 3ti + 8t3/2j+ 12t2 k, 0 sts 1

A: The given curve is: r(t)=3t i+8t32 j+12t2 k ;                0≤t≤1

Q: A) || Jx2 + y2 dA , R is the disk x2 + y? < 9

A: We have to use polar coordinates here.

Q: Q.2) Evaluate x+ y ds where o is the portion of the plane 3r+2y+z 6 in the first octant.

A:

Q: Find the maximum value of f(x,y,z)=D24x+18y+21z on the sphere x²+y2+z²=D49 256.324

A: Given query is to find the max value for f.

Q: Evaluate fR z = Jx2 + y2 x2 + y2 + z2dxdydz, where r is the region bounded by the plane z = 3 and…

A: We will convert integral into spherical co ordinate system . 1st relation between cartesian and…

Q: Sſcos( dxdy y-x y+x D

A: Given and u=y-x,  v=y+x where D is the trapezoid with vertices (1, 0), (2, 0), (0, 2) and (0, 1).

Q: Let f(x, y, z) = x² + 2y? + 4z2. Find the point on the plane x + y + z = 14 at which f has its…

A: Given: fx,y,z=x2+2y2+4z2and the plane equation x+y+z=14 To find the point x,y,z The Lagrange's…

Q: Evaluate f z²dz where C is the contour |z| = 2-

A: We can directly use cauchy Goursat theorem to give the value of the given integral about given…

Q: Evaluate the hutergral sss of dV, where F= (x²-2)i + 208; - 22k and V is the dosed the Planes x=0,…

A:

Q: Sketch a contour diagram for f(x, y) = x2 − 2y2 with three labeledcontours.

A: To sketch the contour diagrams for the given function of two variables

Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: Standardize the cone with equation 7x2+4xy+4y2-8x-12y+9=0

A:

Q: Determine the convexity/concavity property of the following: (ii) f (x, y) = 2x² – y?

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Q: Find of and Duf to :- f cas,z) = In (x²+zy?+32) atp(-v34) in the direction of ã=-3i-4j-12K. -314…

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Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

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Q: re 2" dr + (x* + 2a²y?)dy where C is the boundary of the region between the circles a² + y? = 1 and…

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Q: Use Stoke's theorem to evaluate // curlF - dS where F(x, y, z) = 2y i+ 3xj + (z – x) k and S is the…

A: The given integral is∫∫CcurlF→·dSwhere F→x,y,z=2yi^+3xj^+z-xk ^and S is theportion of y=11-3x2-3z2…

Q: Calculate /| xz dS, where K is the part of the cone z = Va2 + y? where z < 2.

A: Given the surface

Q: Find the coordinates of the point where the line F = (1+21)î + tĵ – 2tk intersects the plane 2x – y…

A: Let's find.

Q: + y² – z dS where S is the part of the cone z? = r? +

A:

Q: Evaluate JJJ, (x² + y²)dV where D is the region that lies above the cone z = c/x² + y2 and inside…

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Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

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Q: (c) Evaluate . 2y² + 4z? ds, where o is the first octant portion of a cone z = Vx2 + y2 with height…

A:

Q: Find the points on the cone z2 = x² + y² nearest the point P(6,8,0).

A: Here, we need to find the points on the cone z2=x2+y2 nearest the point P(6,8,0).

Q: Find the uolume of the region abave the メy- plane inside the cone xZ+y2 glirder and inside the…

A: Convert the parametric form.

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: || x² + y° – z dS where S is the part of the cone 22 = x² + y? that lies between the planes Evaluate…

A: According to question, Given, S is the part of cone Z2 = x2 +y2, it lies between planes z = 2, and z…

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

A:

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Above the cone z = sqrt(x2 + y2) and below the sphere x2 + y2 + z2 = 81

A:

Q: dA, where K is the disk r + (y 2 +?

A:

Q: Jy (a, b)? b.) Determine for what points g(x, y) = x – 2 In|x + y| is differentiable.

A:

Q: Evaluate x2 + y? – z dS where S is the | S part of the cone z² = x² + y² that lies between the…

A: Given, f(x,y,z)=x2+y2-z Here, S is the part of the cone z2=x2+y2 that lies between the planes z=1…

Q: Evaluate ||| Vx² + y² + ²²&V where S lies above the cone z = Vx² +y° and between the spheres x + y…

A:

Q: Find the flux of F = z²k upward through the part of the sphere x² + y² + z² = a² in the first octant…

A:

Q: Compute ,F · dS for F = (xy, 5y,0), S being the cone z² = x + y²,x² + y? 0, with the normal %3D…

A: The vector field is F=⟨xy, 5y, 0⟩ and the parametric equation of the cone is  Rr, θ=rcosθ, rsinθ, r…

Q: W is the midpoint of VX and Z is the midpoint of VY. If XY = t +41 and WZ = t, what is WZ? %3D W WZ…

A:

Q: Find the extremum of f(x,y) = 5x²y² +4y² + 6x². %3D Answer:

A: The given function is f(x,y)=5x2y2+4y2+6x2 .......................... (1)

Q: Find the points on the cone z? = x² + y² that are closest to the point (4,2,0).

A: Given :       z2 = x2 + y2  at (4 , 2 , 0)   Minimize the distance function is   f(x ,y ,z) =  (x -…

Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

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Q: (c) Evaluate . 2y2 + 4z2 ds, where o is the first octant portion of a cone z = /x? + y? with height…

A:

Q: ind the average height of the (single) cone z = sqrrt(x2 + y2) above the disk x2 + y2&lt;= a2 in the…

A: Given equation of cone is, Bounded by the disk,

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

A:

Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

A: