Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the origin. O (1,-1,1)

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A:

Q: 1. The solid that is above by the paraboloids z = 2- x² – y² and below by the paraboloids z = x? +…

A:

Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: 13 - x² – y? at (3, 2, 0), then If the point (1, 1, k) lies on the tangent plane to the paraboloid z…

A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

Q: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

A:

Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

A:

Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

A:

Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

A:

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

A:

Q: 4. Where does the curve r(t) = ti + t²j+ (3 t2)k intersect the paraboloid z = x2 +y² ?

A:

Q: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

A:

Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

A:

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Lagrange's multiplier method uses the system of the equations obtained from the partial derivatives.…

Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: The plane x+ y = 1 intersects the paraboloid z = in a parabola. Parametrize the whole parabola using…

A:

Q: Find a parametrization of the paraboloid given by f (x, y) = x 2 + y2.

A: To find a parameterization of the paraboloid given by: fx,y=x2+y2

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Using Lagrange Multipliers with Two Constraints

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

A: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

Q: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

A: Given ellipse with centers at (0,0) and two vertices (1,0) and (-1,0).

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

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: 5. Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0,0), (0, 2,0), and…

A: we can evaluate the given integral. ∫∫∫R f(x,y,z) dV =∫∫∫R f(x,y,z) dzdydx

Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

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

A:

Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

Q: 11. Evaluate ([(y+z³ )dS where S is the part of the paraboloid x = 4- y – z² that lies in front of…

A:

Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

A:

Q: The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution, Find the…

A: The given equation can be written in the form of the Clairaut's equation as below: z=px+qy+121+q2q…

Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

A:

Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

A:

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

A:

Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

A:

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

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 the absolute maximum and absolute minimum of the function f (x, y, z) = x³ + 2y along the curve…

A:

Q: 8. Evaluate x dV where E is the solid enclosed by the paraboloid r = y²+2? and the plane x = 9

A:

Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

A:

Q: Obtain the Solution x, y > 0, xy > 1 of the PDE 2y on the x+y 1 Uxy such that u = x+y 0, ux…

A:

Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

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

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…