f) Given w=(x+y)/(z-3y) , Find dw

Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz + 0. ду

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

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: Find the general dafferential equatron (t) t 36y () - o lol00lution of the general solution y Co) =…

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Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

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Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

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Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If f(x,y,z) = e2x+3y-4z + xyz And x = 3si n(rt) y = 2cos(rt) z = r² + t² af Find at

A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: Solve the homogenous differential equation.

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Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: Given y = Vx – 2Va – 2; Find y'. - |

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Q: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

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Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? %3D Select the correct response:

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Q: If y = t“, then dy 4t³. dt

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

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

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Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Q3 Given that w = x + 2y + z²,x = = ,y = r2 + In s, z = 2r X%3D %3D aw aw and ar Find as

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Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

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Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

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Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? Select the correct response: y 2y O -2y O…

A: Topic:- non exact differential equations

Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

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Q: K is between J and L, KJ= 46, and KL = 47. Find JL. Y f(X) Vx X,

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: (b) / / | /3(x² + y²)dV, where V is bounded by y = 2r² + 2:² and y = 8.

A: The given question seems to be incorrect. The function inside the given square root should be…

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: Fx, y, z) = (10y – az – 5x)i + (3by – x + 8z)k + (z – 5y + 2cx)j %3D a

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Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

A: follow next step

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: The G.S for Əxəy is اختر احدي الدبابات z=cify + 2x) + czf(y- 3x) a. z= Cfy+2x) + czf(y -x) b. z=…

A: The solution is given as

Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.