3- prove that w comport dx =w dy yx 23 34 if w=: w = xy² + x³y² + x³y

Q: find extreme Value of function fex, y) = x°t 3xy?-3x²-3y=t7 1

A: Given:  fx,y=x3+3xy2-3x2-3y2+7 ⇒fx=3x2+3y2-6x, fy=6xy-6y To find extreme points put fy=0, fx=0…

Q: .3 If U = 2– x, | x 2-xdx=

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Q: Show that x +2 and oe) = *+6

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Q: -t,x-1 dt

A: Please see the explanation below

Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: 2. / Vy² – 4y + 10 dy

A:

Q: then find x²°u +2x)y əxəy If u = (x – y)f(y/x), a2u then find x2 dx2 a2u + 2xy дхду

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Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

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

A: A detailed solution is given below

Q: If fxy (x, y) = , ,0 2) =

A: Given,fXY(x,y)=x+y27 ; 0<x<2 , 3<y<5

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

A:

Q: If fxy (x, y) = y for 0 2X - 2) =

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Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: Show that C=-λR.

A: Detailed answer shown belowExplanation:

Q: If V2 1 1 dv = x V2 V1 \V¼ V½) V2 Зпх -dv =? 1 2T7(V + ny) V1

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Q: Q2. If w = f(u, v) , u = cosx and v = sinx, show that: (30 Marks) d?w = v? fuu + u² fvv – 2uvfuv –…

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Q: Evaluate 1 z-y zy dxdzdy y

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Q: Let X-(1,0,- 1,-V2). Then, |X|l3 = %3D Select one: a. 2+2/2 O b. C. 2 O d. arch

A: Answer :

Q: dw if w = yVx² – y

A:

Q: Let f(x,y) = 9 e2*y, then fxy 18 e2xy + 36xy e2xy

A: The denotation fxy represents the partial fraction of f(x,y) which is found as follows.…