Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

Q: 2. Consider the PDE u; - t ux+tu=0 for - o <x< ∞ and 0 <t< ∞ with u (0, x) = sine x. Determine u (t,…

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Q: Let f(x, y, z) = In(x² + 2) + y²e== – cos(2yz). Find fzyz- %3D

A: Given that: f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: a2 If a;j = aji (ajX;X;) əxyəx; are constant, calculate %3D

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Q: Use this result and the chain rule to find (Isinx|) pr all x € (-T, T),x + 0. dx

A: Given,           ddxsinxWe know that,             The derivative of absolute function is given by…

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Find Wr 0 if W = f(x,y) x=r cos 0 and y = r sin 0, then prove that r Wr 0 =yfx + xfy + xy(fyy-fxx) +…

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Q: dz If z = x.f(xy), express x - Y ze in its simplest form. CS Scanned with CamScanner

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Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: Consider the functions z =2e* In y, x In (u cos v), and y= u sin v. dz (a) Express and du dz as…

A: Since you have posted a question with multiple sub-parts, we will solve first two subparts for you.…

Q: 59. Prove the general formula iwollo oi ons dx 1 x - In x – b + C %3D (x – a)(x – b) a – b - - where…

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Q: az az Use the chain rule to find and as at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az %3D…

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Q: 6. Use Green's Theorem to evaluate (y- ry') dr + (2- r) dy where C'is shown below. x +y =

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Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: Let h(y) = In(y In y). Find h' (y). Show your work.

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Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: Given:         8y3+x2=1dxdt=2x=3y=-1 Differentiate 8y3+x2=1 with respect to t,…

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: Show that u(x, y) is harmonic in some domain. u(x, y) = 2x – x³ + 3xy?

A: since Uxx+Uyy=0, then U is harmonic

Q: ldéntities will prove useful in achie Exercise 12. Show that E, (T: – ¤) = 0 %3D | E (*: – µ)² = E…

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: 4. Use Green's Theorem to evaluate | xy dx + (1 – xy°) dy where C is shown C below. y (1,4) (-1,2)…

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Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: 3. Let z = x?y + 3xy+ where x = sin 2f and y cos t. Use the chain rule to dz find when t = 0. dt

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

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Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: HW.8. Use farseval's theorem to find if f(t)=A e-alti Ans: A?

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Q: 1. (a) Let f(r,y)- cos(z + 2y). Compute the diectional derivative Df(r,9), where u- (b) Compute ff,…

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Q: de dx -KA- = Qgiven that 0(0) = 0₁ and 0(t) = 02 then show that = 0₂-01 t -KA-

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Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

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Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

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Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

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Q: Let z = x*y + 3xy* where x = sin 2t and y dz find = cos t. Use the chain rule to %3D when t = 0. dt

A: z=x2y+3xy4where x = sin 2t and y = cos t We need to find dzdt when t =0 Let's use the chain rule :…

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

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Q: Determine the of : In (xy²) = x y dx

A: Derivative dydx of equation  lnxy2=xy

Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

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Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Use Green's Theorem to evaluate Se xy dx + (1 – æy³) dy where C is shown below y (1,4) (-1,2) 2 1…

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Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…

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Q: 2. Consider the PDE u -t ux+ tu =0_for - ∞ <x< ∞ and 0 <t< ∞ with u (0, x) = sine x. Determine u (t,…

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Q: Show that there exist constants 0 < A < B <∞ such that, for every y, z ER with A В 1 dx < ly – z|3…

A: We need to prove that there exist positive and finite constants A≤B such that, Ay-z13≤∫ℝ1x-y23…