Determine the orthogonal trajectories of the family of electric field lines described by the family (x-c)3 + y2 - c2 (3x-c) = x3

Q: of Q tind diretion derivative of 2メ×+sin ++ll tnthedirection of vector 3.

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Q: Find the orthogonal trajectories of the family of curves y^3 = 3(? − ?). Draw a few representative…

A: We will find out the required solution.

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Find the orthogonal trajectories of the curve family ?

A: Given equation: y=x-2+Ce-x

Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

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Q: 4. x( 4x + 3y) = a

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Q: Calculate the derivative ,11z d da Ja7 In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the orthogonal trajectories of the family of curves y = ax² + 4ax + 4a, where a being…

A: Orthogonal trajectory: If a curve cuts every member of a given family of curves at right angle, then…

Q: Use a linear approximation to estimate V65.

A: 653

Q: Find the orthogonal trajectories of the family of curves.

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Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

A:

Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: Calculate the directional derivative direction Q(5,4) 4 3√-3x²-5xy3 of at P (1,-2) in the

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Q: y = 3x – 1 + Ce-3x | x = Cey?

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Q: Find the orthogonal trajectories for the family of curves x2 − 2y2 = C . Use a graphing utility to…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios…

Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: Vz²+1 ev° dy In a

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Q: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: Find the directional derivatives of Ø = x2yz + 4xz2 at ( 1, -2, -1) in direction 2ax – ay – 2az.

A: Answer is in step 2.

Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: 10. y = Ce 2x

A: We have to find  orthogonal trajectory

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

A:

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: Еxample 5 1 1- Vxdx ха 0,

A:

Q: 4. x*( 4x + 3y' ) = a

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Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…

Q: determine the equation of the orthogonal trajectories of the following families curves: Straight…

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Q: 4. x(4x? + 3у?) -а = a

A: Solution is given as below:

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: 8. The cissoids, y = x°/(a - x) %3D

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Q: In what directjon from the point ( 1, 3, 2 ) is the directional derivative of 6 = 2 xz-y a maximum ?…

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Q: se Cauchy-iemman equations to now that each of these functions is where cnalytic Rz= メ

A: Given: fz=xy+iy   -1 The objective is to show that the given function is nowhere analytic.

Q: 9. y = x'(1- cx ) %3D

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Q: Find the perpendicular trajectories of the family of y = ax" curves. N= -1, n=1 and Draw each curve…

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Q: Find the orthogonal trajectories of the family of circles through the origin with centers on x axis.

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Q: 10. у%3D V2x+1

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Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Find the equation s for the perpendicular trajectories of the curve family. 1. x -

A:

Q: Find the orthogonal trajectories to the family of curves: -1).

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.