Q1/ (A) If w= (x?+yz+Z?). Find m such that W = Wxx + Wyy + Wzz=0 Ans. n= -//2 %3D (B) Use Lagrange multiplier method . De termine dimensions and maximum area of a rectangle that must be inscribed inside the ellipse x2/a2 + y2/b2 = 1

Q: y' = /2y – 1, у(1) — 1.

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Q: 2. For the same problem, use Lagrange multipliers to maximize the volume V ryz under the constraint…

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Q: Q1: Use Newton - Raphson method to estimate the 3 Yoot of fcx) = X- X - 1 , employing an initial %3D…

A: To find the root of fx=x3-x-1 by using Newton Raphson method with initial guess of x0=1.

Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: 1. Find the orthogonal trajectories of the given family of curves: a. y = Ce-mx; with m held fixed

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Q: Find a homogeneous LDE with constant coefficients that has y= - 3xsin2x as a particular solution.

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Q: Find the extreme values of f(x, y) = x² + 2y² subject to xy = 4 using Lagrange multiplier method.…

A: Here we have to use the Lagrange multiper method

Q: Cons i der the linearsystem X2 1. 2. is Gauss-s eidel method

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Q: Use the Newton Raphson Method with XO=[-1 -2 1]' to approximate the solution to the given nonlinear…

A: Given a nonlinear system, Let  fx1,x2,x3=x13+x12x2-x2x3+6gx1,x2,x3=ex1+ex2-x3hx1,x2,x3=x22-2x1x3-4…

Q: 4+ Out X=U -3n,t Ox-2n3=6 + Yx2-2n3

A: x1+0x2+x3=4............i-3x1+0x2-2x3=6........iix1+4x2-2x3=-3............iii Now, converting given…

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: 2. Use the method of variation of parameter to solve the nonhomogeneous system X' = AX + F(t) where,…

A: X1=AX+F(t)A=1232    F(t)=2te2tThe characteristic equation of…

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: Use Runge-Kutta method of order four with step-size h = 0.5 to approximate the solution for 2<t<3 of…

A: given IVP isdydt=-y+ty1/2y(2)=2h=0.5here dydt=f(t,y)where f(t,y)=-y+ty1/2t0=2y0=2h=0.5by using R.K…

Q: Solve the nonhomogeneous IVP using the method of undetermined coefficients: y" +4y = x - 2cos 2.x,…

A: To solve the given Homogenous IVP using the method of undetermined coefficients.

Q: 8.9. The volume V of the liquid contained in the spherical tank of radius r is related with the…

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Q: Consider a circle of radius 2 centered at the origin. Use the Lagrange multiplier method to find the…

A: It is given that circle is of radius 2 and centered at origin. The function isfx,y=3x-y+5.

Q: 2. For the same problem, use Lagrange multipliers to maximize the volume V = xyz under the…

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Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: Q1: Use ewton- Raphson method to estimate the Yoot of fcx) = x -x -1 , emp loying an initial %3D…

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Q: (6) Find the orthogonal trajectories of the family of curves y = ax? + 4ax + 4a, where a being…

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Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

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Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

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Q: (ii) Find the extremum of Z= x2 +y2 subject to x + 4y 2 and examine whether the %3D %3D stationary…

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Q: Use the Newton Raphson Method with XO=[-1 -2 1]" to approximate the solution to the given nonlinear…

A: To find - Use the Newton Raphson Method with X0 = -1 -2  1T to approximate the solution to the given…

Q: 2. Consider the following (knapsack) LP: = 150r1 + 100x2 + 99x3 51x + 50r2 + 50r3 S max z 100 T1,…

A: We find the solution of the given linear programming problem we first find the solution of the…

Q: Given the one-parameter family of curves y² = Cx³ + 5. Find the family of orthogonal trajectories.…

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Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

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Q: find the suprimum, in! infimum maximum and minimum of { c,1": (1+):ne w}, if t)ine w}

A: Supremum: Let A⊂ℝ then, least upper bound of the set is called supremum  of the set A. Supremum may…

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

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Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the extreme values of f(x, y) = x² + y² subject to the condition x²y = 1 using Lagrange…

A: solution is given below..

Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4x + 5y = k (2) 4х — 5у 3Dk…

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Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

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Q: 1. Find the orthogonal trajectories of the family of curve z² + 3y which is passing through (10,…

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: 5. Find the orthogonal trajectories of the family of hyperbolas x² - 2y = ax. %3D

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Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

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Q: Use the Newton Raphson Method with X0=[-1 -2 1]" to approximate the solution to the given nonlinear…

A: Solution: The system is x13+x12x2-x1x3=-6 ex1+ex2-x3=0 x22-2x1x3=4 Suppose that…

Q: 1. Find the orthogonal trajectories of the family of curve z + 3y = cy,where cis an arbitrary…

A: We will first find the differential equation of the of the given family of curves

Q: 3- Find the orthogonal trajectories of a system. x²y² – 2xya + a = 0 %3D

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Q: Use Lagrange Multipliers to find the absolute maximum value and absolute minimum value of the…

A: We have to find absolute maximum and absolute minimum value for the given function.

Q: 1.8 1.6 S (3-2) (7- y²) dz dy -1.8 –1.6 using an adaptive Gauss-Legendre Quadrature method.

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Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k