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

Q: Let y = x. Find dy and Ay at a = 8 with dx = Ar = 1. dy Ay =

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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: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: If y is implicitly defined as a function of e by –2 + + cos(y) = 3, determine de ysín(oy) + 2 -1…

A: We have to find dy/dx.

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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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: 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: When reduced to a linear DE of order one in z, the Bernoulli's equation dy 2 +y √( 1 ) = 3x²y² =…

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Q: 27. w = xy + yz+ zx, x = r cos 0, y = r sin 0, % = r0; %3D dw dw when r = 2,0 = T/2 Ər' d0

A: Given that,  w=xy+yz+zx , x=rcosθ, y=rsinθ and z=rθ. To determine the value of ∂w∂r, when, r=2 and…

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

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

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Q: So** f(x, y) dy dx + Le-1)* f(x,y) dy dæ = %3D elect one: O a. f S f(x, y) dæ dy O b. None of these…

A: To find the addition of two surface integrals by changing the order of integration gives the result.

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: 1 Let y = -. Find dy and Ay at x = 8 with dx = Ax = –1. х Enter the exact answers. dy = Ay =

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Q: 17. Evaluate the line integral xe" dx +y sin yªdy along the triangular path consisting of the line…

A: Consider the given integral. I=∫Cxex2dx+ysiny2dy The given points are 0,0,2,3,1,0,0,0. Now, draw all…

Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

A: We have to find the value of  ∫Cxy dx + y2+1 dy. Given the path C is

Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

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: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

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

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Q: 1 2 _2 If U= +¯ +y¯ +z¯ is not equal to 0 then prove x+y° + dU + du that dx = 0 dx dy

A: Given function is U=1x2+y2+z2. We have to prove  d2Udx2+d2Udy2+d2Udz2=0

Q: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

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Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

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Q: dz Let z=e"In(xy), determine dx et (1+xin(xy)) dz A %3D дх az (1+xyln(xy)) %3D дх y (1+yln(xy)) %3D…

A: Explanation of the answer is as follows

Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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

A: Let's find.

Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

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Q: dy Reduce the linear DE (2xy+x2+x*)dx- (1+x)dy=0 to standard form + yP(x) = Q(x). dx 2х +y |=x2 A dx…

A: Differential equation

Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

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: 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: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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Q: xy*-dy = (a* lIn a – y (а* In a - y %3D

A: we have to find the differential of ax=y

Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

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: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = , y=t, z= t'

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Q: Let y = -. Find dy and Ay at x = 9 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

A: Solve by using differentiation