24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1).

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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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: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

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A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

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

A:

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: dy -y2+1,ysCJse Cantial cokditian.

A:

Q: x+ y dydx = Inß ху %3D Find B.

A: The objective is to find the value of beta.

Q: I need help with 1a)

A: straight line becomes y=x

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A:

Q: 3r'e" dx+ 5x'e" dy C:boundary of the region lying between the squares with vertices…

A: Given integral is ∫C3x2e2ydx+5x3e2ydy Since boundary of region lying between the squares with…

Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Find dy/dx if y = x^3/2 by using the Chain Rule with y as a composition ofa. y = u3 and u =…

A: a) y=u3 and u=x     dydu=3u2anddudx=ddxx       =12x-12 So, dydx=dydu×dudx      =3u2×12x…

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: find the dy/dx at x=-2 for y=3u^2 + 2u and u= (x^2+5)^1/2

A: Explanation of the solution is given below....

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: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: 2-if (x - y) (x + y) = 1 prove that d²y + y dx² (2x)² = 1 dx

A: Topic:- application of derivatives    Note:- as per our guideline if more than one question uploaded…

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

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Q: 4) (у-сos' x) dx + cos xdy %3D0 5) 2y(y² - x)dy = dx

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Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

A:

Q: 21. xy' = 3y +x* cos x, y(27) = 0 22. y' = 2xy + 3x² exp(x²), y(0) = 5 = 4x* %3D %3D %3D %3D 23. xy'…

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Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

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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: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

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Q: H.W: Solve-Using D-operator dy dx + dt + 3y – 5x – e-t = 0 %3D dt dx dy + x + y - 3 = 0 dt dt 2.

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Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

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: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: Find the I.F of y(2x-y+1)dx+x(3x-4y+3)dy=0.

A: Given equation is y2x-y+1dx+x(3x-4y+3)dy=0

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

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

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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: Let z = exsec y Find d²z dxdy and d²z dydx

A: .

Q: Find y' and y". y = Vx In y' y" %3D II

A: we have ,  y=xlnx y'=?y''=?

Q: dy find 3 - x x - 2 1) If y = t + 2t , t = %3D %3D dx

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

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

A: