Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス) -2 @ Calculate the Jacobian mutrix J andj' O Compule J

Q: Sketch the Part of tthe slope Field of y'=L for X and y be tween -5 and 5. Then add to your sketch…

A: Slope field of y' =1/y

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

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Q: Given that U is a function of x, y and z and A a vector field, prove that: V x (UA) = (VU) ×A +U…

A: We will use definition to solve this.

Q: The gradient of a scalar field V is a vector that represents both magnitude and the direction of the…

A: Given : The gradient of a scaler field V is a vector that represents both magnitude and direction…

Q: How do you compute torsion?

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

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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: Determine if the function satisfy the Cauchy-Riemann equations. Show your soluition. 6. f(z) = z?

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Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

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Q: Let f(z) = z2 is f(z) satisfy Cauchy-Riemann equation ?

A: Let any complex function f(z) = u + i v then it satisfies Cauchy-Riemann equation when 1) ∂u∂x=∂v∂y…

Q: A pasticle depicts ts motion in Such a ulay at time ť is P=xîty where, 2= acoskt and y=bsinkt. that…

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Q: Find the orthogonal compliment to S span{ 0 }. ||

A: To find the orthogonal complement to S spanned by two vectors .

Q: Soru 5) y' – y²secx + y tanx – cosx = 0 Riccati diferensiyel denkleminin bir özel çözümünün y1 =…

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Q: Prove that div(x) .curl - curl w functions. 11 where and ware vector

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Q: please solve this question

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Q: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

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: 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: Explain the meaning behind the expression foF-dr, for a curve C and vector field F.

A: To explain: The meaning behind the expression ∫CFdr for a curve C and vector field F.

Q: (1 point) Show that the vector field F-yz Ч + zz 1 J-zuz 2 k is conservative by finding a scalar…

A: To find the scalar potential function f, assume

Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: Determine una ecuación del plano tangente a la superficie dada en el punto especificado *:(-4, 2,…

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Q: b) Use chain rule 1 - arctan u, where u = e* y =

A: Given y=1u - arctan u, where u=ex apply derivatives on both sides…

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

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Q: .) Find the work done by field F = (-y,-x) along curve C: counter clockwise along semicircle y = v4…

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Q: Calculate div(F) and curl(F).  F =〈x^2, y^2, z^2〉

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Q: 10. Para resolver la siguiente ecuación diferencial: y" + 2y' + y = 0 con y(0) = 1; y'(0) = 1 Se ha…

A: The solution of differential equation is given by using Laplace transform and partial fraction…

Q: azu azu (a) Verify that u satisfies ax2 = = 0 , if u = e* sin y. ay?

A: NOTE:Kindly repost the other question as a separate question.

Q: 5, find dt when r = 3. dt Let A be the area of a circle with radius r. If %3D %3D

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Q: what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)  (show all steps…

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Q: rest from the right vise with an accelera mains constant. Fin

A: The acceleration (a) of the particle is 0.25 m/s2. The body accelerates from rest until a time of 4…

Q: (4) Find the -periockic points and detorimme their sta. stakliny of hu)=EX %3D

A: 4) Given: h(x)=1-x3x+1 Determine the periodic point by substituting h(x)=x.…

Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: Therefore, div(curl G) = sin(y) – sin(y) + 8 = Since div(curl G) is different from 0, we conclude…

A: Given that:div(curl G)=siny-siny+8=

Q: cotu. vX + vy + y %3D If u = show that x ax ay = CoS coS х - у

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Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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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: Define whot ore Conservotive ond non- Conservotive vector Sive on exomple of conservative force ond…

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Q: write the line thraugh y S.0;?) (5,0, in the dircetion of 2 vcetor parametruc امپري؟

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Q: 6. Show that the system with vector field -x + sin(y) F(x, y) : -y+ cos(x), admits no periodic…

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Q: Show that if |sin z| is bounded along the straight line {(x, y) : ax - By = 0}, then a = 0, i.e.,…

A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1),…

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Q: Use a linear approximation to estimate V29. Show the work. Do not round your

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Q: that F(x, y, z)= Divergence Theoren

A: The given vector field is Fx,y,z=xz2+12.13, sin y, x·y5. The upper hemisphere can be taken as…

Q: Prove that divergence of vector potential 'A' is always zero.

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Q: Show that f (z) = e? is not analytic using Cauchy-Riemann equations.

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