22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of vecfor U = 2€ +j-2k-

Q: 2. Prove that fo r*dr + xydy = -+- where C2 is the line segment from (1,0) to (0, 1) by using…

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Q: (c(2z+y), %3D ue of c in the joi F of W.

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Q: Obtain the DE based on given conditions solve for item 1 only.

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Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Let y = 2x + 2x +3. If Ar = 0.2 at a = 2, use linear approximation to estimate Ay %3D Ay Submit…

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Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: Find the uolume of the soild olbtained by the grophs bounded by potaling the begion Y = x² +1 and Y…

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Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

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Q: Show that f(z) = x ² + y ² where z = x + iy is not analytic anywhere using Cauchy Riemann equations.

A: Cauchy Riemann Equations: Given,  f(x+iy)=u(x,y)+iv(x,y)  and it should satisfy  ∂u∂x=∂v∂y and…

Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

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Q: The vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

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Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: Find equations for the tangent plane and the normal line at point Po (X0,Yo,Zo)(1,5,0) on the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4   Now we know that the rate of change is simply derivative…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Find vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: dz - Prove that : Iz%3D2 %3D z%3D2 z+1 2in.

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Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: A body of mass 6 kg moves in a (counterclockwise) circular path of radius 6 meters, making one…

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Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At…

A: Given Motion is a circular motion. r = radius of the circlea = x-cordinate of the centreb =…

Q: Find the orthogonal trojectories of y(sx +c) = 1.

A: Given query is to find the orthogonal trajectories to y (3x+c) = 1.

Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

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Q: curve in the xy-plane is denned by the vector valued functic dy in terms of t? dx? where x(t) = 2…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Given problem is :

Q: Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant…

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: A point moves along the intersection of the elliptic paraboloid z = 6r + 7y and the plane y = 2. At…

A: Given: A point moves along the intersection of the elliptic paraboloid z = 6x2 + 7y2 and the plane y…

Q: 16. The solid within the spherex² + y² + z² = 9, outside the cone z = Vx2 + y², and above the…

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Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 4y and the plane y = 4. At…

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: The plane tangent to the surface z +1= re" cos z at (1,0,0) can be represented by the equation X + y…

A: Given: z+1=xey cosz

Q: Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y2 and…

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Q: 2dy -2y 2. zt at

A: Solved below

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: L'équation 5xyz = 2x2 + y² +2z² + 6 définit implicitement z comme fonction de x et de y au voisinage…

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x =…

A: To find: The parametric equations for the tangent line to the curve of the intersection of the…

Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

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Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.