Generalize What do you notice about the corresponding coordinates of the preimage and mage after a reflection across the x-axis? © MP.8

Q: Find the orthogonal trajectories of the family of curves y=Ce* +10

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Q: 5. Show how the origin changes stability as a changes by using the Poincaré Diagram. x - [i :]• 2 a…

A: The stability of fixed points of a system of constant coefficient linear differential equation of…

Q: If f(3) 12 and f '(x) 2 1 for 3 sxs 7, how small can f(7) possibly be? Enhanced Feedback

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Q: 2ys = Cx

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Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: 35. Give linearly independent functions that are annihilated by D² (D² – 2D + 10).

A: We will find roots for the equation and use concept of differential equations to find the linearly…

Q: Find the orthogonal trajectories of the given family of curves x - 4y c.

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Q: b) Find the orthogonal traJec tories of the families o f r=5acose where la) parameter

A: We have to find the orthogonal trajectories of the families of r=5acosθ where a is parameter.

Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y-3 = C

A: In this question we have to eliminate the arbitrary constant on the given equation.

Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: find the orthogonal trajection of the family of curves x2+y2=a2

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Q: (b) Use a calculator to verify that Ex = 150.4, Ex² = 3251.86, Ey = 250, Ey² = 10630 and Exy =…

A: a.) The scatterplot of the data is

Q: Find the linearization of y = eV1x at x = 36. (Use symbolic notation and fractions where needed.)…

A: We have to find linearisation

Q: 1. Find the following. Iy(-1, –1) if g(x, y) = x³ – xy² + 3

A: Given g(x,y)=x3-xy2+3 Differentiating g partially with respect to y, gyx,y=∂g∂y=0-x(2y)+0…

Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

Q: 2. Find the family of orthogonal trajectories of the given family of curves in the following…

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Q: You have the following data poi 40.2 12.3 2.00 4.00 You wish to detemine the value Y-2xis label:…

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Q: (b) Determine e so that п п c£[(x; - X;)² i=l j=1 is an unbiased estimator of o². s2 ogunl to

A: 6. From the given information, X1,.....,Xn~f be an iid random sample with mean μ and variance σ2. a)…

Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: What are the control points of the splines Bezier curve from the two equations given below: a(x) =…

A: Given, ax=1+5x2+2x3...1bx=1-x+x3...2 The control points are lie on both the curves. So, to get…

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: 7

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Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 7. x = 3(y – c);

A: Here we have to find the orthogonal trajectories of the given family of curves.    x3 = 3(y-c)

Q: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

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Q: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y- C

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Q: (6) Find the orthogonal trajectories for the given families of curves 2x2 – 7y = c.

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Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x°(1– cx);

A: We have to solve

Q: y6 = C (x² + 1) %3D

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Q: I Example 8.24. Using three point Gaussian quadrature formula, evaluate * dx q85 Jo 1+ x

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Q: Find the orthogonal trajection of the family of curves x2+y2=a2

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Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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

Q: The ops y' =esx-7Y;s Separable

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Q: Which of the following is the orthogonal trajectories of the family of curves y = ax³ ? x³ + 3xy² =…

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Q: Given that g(2)=5 and g'(2)=3, linearize g(x) near x=2 and use this linerization to approximate…

A: Consider the linearization formula for g(x) near x = a.

Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: 8. DETAILS SCALCET9M 3.10.003. Find the linearization L(x) of the function at a. Rx) = Vx, a = 64…

A: given,

Q: Q5: S x dx ajconverges to 1 bjconverges to cconverges to- 4. d)diverges 25-2

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Q: Which of the following is the isogonal trajectories of the one-parameter family of curves y(x-a) = 1…

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Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x*(1 – cx);

A: The given equation is y2=4x21-cx. Find the orthogonal trajectories of the given family of the curve.

Q: (b) Classify the equation t - 2ty +2y =t, t> 0. What order is it? Is it linear or nonlinear? Is it…

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Q: min ||y – Hx|3 + A ||x||3 x = (H'H + AI)-1H'y (18) In reference to (18), why is HTH+ AI with A > 0…

A: Given - minx y - Hx22 + λx22 ⇒ x = HTH + λI-1HTy           18 To find - In reference to (18), why is…

Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…