OFind the orthogonal Tradectories of the families of y2-5ax 42 - %3D where a being a Parameto

Q: 1. Prove that fo r*dr + rydy = where C1 is the line segment from (0,0) to (1,0) by using…

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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: Find a parametrization for the cylinder x2 + y2 = 1.

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Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

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Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A) Determine a…

A: Solution of the system of equation will give the equation of the line of intersection.

Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Integrate ƒ(x, y) = sqrt(4 - x2) over the smaller sector cut from the disk x2 + y2 <=4 by the…

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

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Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: Give a parametrization, including the appropriate u- and v-bounds, for the portion a cylinder of…

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Q: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

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

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Q: find a parametrization for the curve. the ray (half line) with initial point (-1, 2) that passes…

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Q: Consider uxx + auxy – 2uyy + ux + 2uy = 0 Find all values of a so that the PDE is Hyperbolic.

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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 a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: Find the orthogonal trajectories on the sphere x2 + y2 + z2 = a2 of its intersection with the…

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Q: Compute paramenc curve Ogiven by bu Iine of the X= eEsinct) 二e ato t=

A: To Determine: Compute the tangent line of the parametric curve given by  Given: We have   x=etsint…

Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

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Q: 2. Bounded by the paraboloid = 10 – 322 – 3y? and the plane z = 4 (using polar coordinates)

A: The paraboloid is bounded by z=10-3x2-3y2 . Now, converting in polar coordinates, z=10-3r2.

Q: Use the method of Lagrange multiplier to find the 3D vector lying on the intersection of hyperplanes…

A: let u=x i+y j+z k be a 3D vector lying on the intersection of hyperplanes x+y=2 and y+z=4 that has…

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

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Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: Find a vector function that represents the curve of the intersection of the two surfaces. The…

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

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Q: Find the least squares quadratic & bj xj which best fits curve Y = sin(x)

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Q: 3. Find an equation of the tangent plane to the paraboloid defined by z= 5x +4y? at the point…

A: The given equation is; z=5x2+4y2 at the point (-1,1,9).

Q: find a parametrization for the curve. the ray (half line) with initial point (2, 3) that passes…

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Q: The tangent plane to the elliptic paraboloid z = 2x2 + y² at the point (1, 1, 3) is %3D 1) 8x + 6y +…

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Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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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: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: find ⌠⌠F*dS if F(x,y,z)=2xi+2yj+2zk and S is the paraboloid z=8-x^2-y^2 lying above the rectangle…

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Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

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Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.