Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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Q: dA Calmilate Je= JJ Jxtxyz behween ay?sl6, x?ey?s1 and unde y=2.

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Q: Find (3x + y)dA where D = {(x, y) | æ² + y? 0}

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Q: y" – 7y' + 12y = 3t?e4t – te3t sin t -

A: Given:  y''-7y' +12y =3t2e4t -te3tsint

Q: Vx.y" +x = 4, y(0) = 1, y'(0) = 11 %3D %3D

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Q: Q3:- Find fx, fy if f(x, y) = y+cosx 2y %3D dw

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Q: TW is the midsegment of the trapezoid UVXY. If XY = 20 and TW = 30, what is UV? Y U W V UV = Submit

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Q: Find y' and y". y = Vx In(x) y' = y" II

A: Given query is to find first and second derivative of the expression m

Q: Find V x² +y dædy, where A{(x, y) E R; ² + y < a?}

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Q: d'y 2y If x + y = xy, show that dx2

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Q: (c) S, y*/1- y² dy

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Q: Evaluate: xyze-(a+y+z) dxdydz 0.

A: The given problem is from the calculus and subcategory triple integration here in the given question…

Q: dy 24. Find dr? in terms of x and y. 6-8xy 9x-5y %3D

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Q: (3 da + dy = 0, y(-1) = 2. (y-2x) ry? %3D %3D 3.

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Q: What is the point on y = 2 Vx that is nearest to (4, 0) ? A) (2 V7.27) B) (2, 2 Vz) C) 2/6 3 D)

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Q: et f(x, y) = 14x² + 13y² %3D nd D = fzz · fyy – fây-

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Q: Solve : dy- (- y) . Inn dy %3D ,13-1 Ordinery Dibberential equetion.

A: Solution:Givendydx=(1-y13)x2 ln xy13-1

Q: f(z, y) = 2 + + 8y? %3D (x, y)D dy dz , y) = (2, y)

A: Given function is fx,y=2+x2+8y2. Differentiate fx,y=2+x2+8y2 partially with respect to x.…

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: c. y" – 8y' + 20y = te', y(0) = 0, y'(0) = 0 %3D

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Q: Dyy 2y-x; %3D

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Q: Find the velocity v(t) and speed ||v(t)|| of a particle whose motion is described by x = 2f² – 8t +…

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Q: show that if y=cosx/x, then d^y/dx^2+2dy/xdx+y=0

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Q: If y = (x + 1)(2x – Vx), then y' will be,

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Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

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Q: Find S y dy y+2 using the substitution V +5=√y+2

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Q: XY = WZ m22%3D36°, m ZW = 57°, find m23

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Q: (a) y(t)=1+af,y(t)dr,1 > 0

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. @ y = (c,+cx)e¯* + cze -2r + e*(c_,cosr + c zsinx)…

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Q: 9. Find y", given y = %3D Vx-1

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Q: Prove that r(v) : dx, v> 0.

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Q: dy of y3Dx dr Find csc2r,

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Q: Given = 8t + 39 and y = 48t + 117 %3D da (i) dt %3D dy (ii)- dt dy (iii. dx (write the simplified…

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Q: Find at (2, -2, 1) if dy x2 + y? + 22 = 6xz + 6yz + 21 %3D

A: Given that x2+y2+z2=6xz+6yz+21 Then we have to find ∂z∂y

Q: (x, v) = (2ry) i + (r – 2rv) j ,2]. -

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Q: Given a = 6t + 18 and y = 27t2 +146 %3D %3D da (*) dt %3D dt dy (write the simplified answer) %3D da

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Q: dy dr² in terms of x and y given that 6- 7xy = 6x - 7y %3D 22. Find

A: Given that ,6-7xy=6x-7y differentiate this equation with respect to x ddx(6-7xy)=ddx(6x-7y)…

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

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Q: J(y) = S. [(2x – 3)²y? – 6y²] dæ, - 3)²y2 – 6y²] dx, Y € C²[a,b] Find

A: Given:

Q: 7 dy (18a* + 16e5)', find da Given y = %3D

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Q: g(x) = Af(Bx), where: %3D A = %3D B =

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Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

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Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

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Q: If x"y" = (x + y)"** m. m+n Then, P rove that dx?

A: Double derivative

Q: 27) メゴキy ke*, y)=o ylı)-0 %3D xe

A: We have given the initial value problem

Q: F (r, y) = (3x²y² + cos y + ye", 2ar*y - - r sen y + xe*)

A: Given F→x,y=3x2y2+cosy+yexy,2x3y−xsiny+xexy. We have to determine whether the vector is gradient…

Q: Given a = 6t+ 18 and y 27t2 + 146 %3D da tf (*) dt cion dt dy (write the simplified answer) %3D da

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Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

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