Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

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Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.

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A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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Q: (b) F= Ewxv(4, 5, 9, 13, 15) + d(0, 1, 7, 11, 12) w,x,y,z

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Q: Sv.Vdxdy = dxdy = ду 2 + JR V.(6,x)-V,(b,x)]áx + [ [7 (a, y) –V,(0,v)ky.

A: Here is the solution of the given problem.

Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

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Q: Let X=(1,0, – 1, - /2)'. Then, ||X||, =| Select one: а. -1- V3 b. -V3 O C. 2 +/2 d. -V2

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Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: Where did F(x, y, z) = Em(1,4,5) come from

A: The steps to follow to write a function in SOP form:    1. Write AND terms for each input…

Q: Find V x (V x F) if F(x, y, z) = 5xyj+ 9xyz k. V × (V × F)

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Q: (b) Calculate dx ds ду ds dz ds II || ||

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Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

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Q: Calculate ffs f(x, y, z) dS For ffs f(x, y, z) ds = y=5-2², 0≤ x, x ≤5; f(x, y, z) = =2

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Q: Q/ If the joint p.d.fof X and Y as f(x,y) = }*y (cx?y ,x2sys1 ,0. W find the value of c and P(x 2…

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Q: 3 For f(x,y) = In x+y°, 4,8)

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Q: Let X=(1,0, – 1,-/2)'. Then, ||X||2 = Select one:

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Q: 9. Find div F if F(x, y, z) = x²yi + xyzj - x²y²k. A. 2xy + yz - 2xy² B. x² + xy C. 2xy - xz D. 2xy…

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Q: Let f(x, y, z)= and c(t) = (t, 13/2, t). Compute ff ds y+z

A: The given function is fx,y,z=x+yy+z, and the curve is given by c(t)=t,23t3/2,t. To Evaluate:…

Q: Z eXZ 4. xyz dydx dz

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Q: 5. Let w = f(u, v), where u = x + y and v = x - y. Show that дw ди дх ду = () - ( ) 2

A: Given, w=f(u, v) where u=x + y and v=x - y To prove: ∂w∂x∂w∂y=∂w∂u2-∂w∂v2