Which of the following are linear transf sua T:P2 Pa where T(p(x)) = x³p'(x) %3D S:M2x2 + M2x2 where S(A) = -AT 3x+у- 1] x+y+2. %3D R:R2 R2 where R -> a. Tonly O b. Tand S only c. S only d. R only

Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: dx 1) S- x(Vx+Vx?)

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Q: + 5)3; 3. dy

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Q: 5. y' = -4x/y, y(2) = 3 %3D %3D |

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Q: Find dF dx and dy Fle,y) =x?+ 3x4+4-1 at the 2. paint (4,-5)

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Q: dy Find for 3(x2 + y²) ² = 100xy dx

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Q: Evaluate: d dxJ (21² + 5)² dt.

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Q: dx tan x -1 '+ 4dx de x- Vx

A: Taking #5 and #6 As per authoring guidelines, if the question number is not specified, the first…

Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: dy Differentiate implicitly to find 6 5 3) x y+9x = 6y +4 dy

A: A detailed solution is given below

Q: Find y": Vy - Vx = Va

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Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: 2. +x +1 d

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Q: dy (1 + æ)* Find for y dx Ans=

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Q: 1 dx Vx(1+ x)7

A: ∫1x1+x52dx