x2 B) If w = x".f then show that: %3D x. Wx + y. Wy = nw.

Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other…

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Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: y= e fonksiyonunun d'y dy 11 + 27y = 27e dr 11z dr?

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Q: If f(x, y) = x cosy + ye*, find a2f дхду

A: Partial derivative: A partial derivative of a function is defined as the derivative of the function…

Q: 2) Prove that: a) dx' dx- b) F) = dF %3D Ldx dx c) [x,p²]= 2h?d/dx

A: To prove- ddx, d2dx2= 0 The mathematical definition of commutators is, A, B= AB-BA Given, L.H.S.…

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Q: If Sdx = s ( + g(x)dx, then A + f 9(2) dx is equal to %3D

A: ∫x2-1x3+xdx To break the fraction we use partial fractions…

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Q: Trapezoid JKLM is shown below. y 4 К (2, 3) L (4, 3) 1 (1 1) M(5 1) 3. 2.

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Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

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Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: af If f(x) = x²yz + xy³z than is дудz x?yz + xy°z yz + y°z Option 1 Option 2 x? + 3xy? y? + 3xy?…

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Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

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Q: Evaluate * ISS 9z dV E where E is enclosed by z = x? + y? and z = 1 4JT O 3T O 27 ол

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Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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Q: esing pyphagoras th, Diff wt to t 2xda +rydy 20 at da dt az3 m

A: Apologies for the inconvenience.   Let, x = the distance from the wall. y = the height of the top of…

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

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Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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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: dy let y = xtan z then is da elect

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Q: dy Find at (x, y) = (3, 4) and z? = a²+y² if d = x² + y? if 1 аnd 2 6. dt

A: Given z2=x2+y2, (x, y)=(3, 4), dxdt=1, dydt=2. When x=3, y=4, z2=32+42   =9+16   =25 ⇒z=5

Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: ize P= 3z + 4y E to 21 + vS 16 27+ 3y S 24 z20, v 20

A: Introduction: Linear programming is the most basic method for optimizing a problem. We can use this…

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: Sm Vx dx

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Q: ..... If F(x.y) = x° + 2x?y - 2y°, then F, = If F(x.y) =x + 2x?y – 2y°, then F, - dy dx

A: We will use various derivative formulas to solve these as shown below

Q: If f(x, y, z) = xy + z?x - 3yx z?, find fxy ?

A: If fx,y,z=xy+z2x-3yx2z2 Find fxy ?

Q: Solve the diffgerential Eauation by Separating the Vaciables ex dy 2x %3D

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Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: 11. If mVQ = (y + 7)', mQR= (x + 11)', mRS = (3y)', and mST = 65', find the values of x and y. %3D S…

A: According to the Bartleby guidelines only one question can be solved at one time, post the remaining…

Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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Q: Given f(x, y) = In(3x² + 5y²) then af dx

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

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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: 11. f (x, y) = ery subject to a? + y? = 16 %3D

A: The objective is to find the lagrangian multipliers for fx,y=e2xy subject to gx,y=x2+y2-16. To solve…

Q: f(x, y) = e&z– 4y af af ду

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Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: f (x, y, z) = xªe²y+æ² zy? – 5zæy³ | af af af dx ' dy' dz Determine

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Q: If Jf(x)dx = cotx? +C, then f(x) is equal to

A: ∫f(x)dx=cot x2+C

Q: Given: f (x, y, z) = 2x'yz² + 5x°y*z® - x³y? ,5_3 Required: fzyx , fxzz

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Q: Find Vf(x, y) if f(x,y) = e** cos y ..... ...

A: