Given: WX || YZ,WX = YZ Prove: AWXZ = AYZX W Z X Y

Q: 1æ² + 4y? + 5z², find 2 Given f(x, y, z) V fz(x, Y, z) = fy(x, Y, z) = f-(x, y, z) =

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Q: Find J, ()dx Chint:let Z=Jx)

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (5t + 8)i + tj, 0 ≤t≤1

A: A line integral is used to find the integral of a function over the vector function. Line integral…

Q: Given: WX 1 XZ, YZ 1 ZX, WZ = YX Prove: ΔWZX ΔΥXΖ Y W

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Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

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Q: Consider the exact U (x,y) that 2x + f = x taf Statistics. au aa au DDE (2x+ f) dx + (x + ² f) df =…

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Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

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Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: Evaluate L"L [II v²z dz dy dx 1 110 110 |110 111 |-111 1 111 1 110 10

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: Name the preimage of R'. T' T V' R' R Your answer: O T O V O R

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Q: Prove that: V- A = -VA

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Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: 5. Prove that |xy| = |x|-|y| for x, y eR.

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Q: Prove or disprove: Vx € Q, Vy e Q, 3z E Q, (x < y) → (x < z< y).

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Q: Compute u X v and v X u for u = jX k and v = kX i. u X v = V Xu =

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Q: Find fr, fre and fy if: f(x, y, z) = xy + yz + xz %3D

A: We have - f(x,y,z) =xy+yz+xz To Find - fxz, fyz, fxy

Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D…

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Q6:-Find aw and ar if as 1) W = x2 + y² 2) W = Ln(x² + y² + 2 ,x = %3D

A: It is partial derivative

Q: 2: find fr, fy, and fz.

A: Given fx,y,z=e-xyz to find fx differentiate with respect to x fx=e-xyzyz

Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: Evaluate y ds, C: x = t, y = t, 0<t < 8 12 (257V257 – 1)

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Q: üx (u x i) = 0 for all u, v in R.

A: we have to identify the given statement is true or false

Q: A regular pentagon is a five-sided polygon with sides that are all equal in length. All three…

A: The solution is given below:

Q: dx and u = 3x-2 1. y 2+1 + 3

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Q: 2. Given V = x + y' av a) Find and b) Hence, show that y ( - ) = v. = V. ду

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Q: 2. Compute ¡ E x dV , where E “ tpx, y, zq | x ď 0, z ď 0, x2 ` y 2 ` z 2 ď 9u

A: The given integral,