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

Q: Let f(x, y) = xy – y³ + x². where u =. O A. 37 O B. -37 10 37 √10 O D. -37 C. Du(f)(1,2)=?

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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 V × (V × F) if F(r, y, z) = xyj+ 6xyz k.

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Q: = f(x,y, z) = x + sin y and Calculate if w ди x = x(u, v) = In (u + v), y = y(u, v) = e".º and z =…

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Q: If w = f(x,y), x = uv and y = u + v, find wuy and wWuu:

A: Answer

Q: SupposeThat w=XYz+XY +Z+3andx=3cost, %3D Y=35int, z=27, Evaluete dwl dtt= I 2

A: solution.

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

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Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: re 'C' is z-

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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: Let w = x +y+ z, x = u³ + v³, y = eu, z = u – v and u = t+1, v = e*. Find the value of w (0). %3D…

A: Given: To find: The value of w'(0).

Q: If r = (2x − x²y)i + (3xz − y²)j − (4xy² + x²z²)k, find ∂r/∂x , ∂r/∂y , ∂r/∂z

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Q: Q3: If z = f(u,v,t) = Z 3u? + v2 ,u = tet , v= te-2t Then dz at (2,2,0) at

A: Topic:- partial derivatives

Q: 3 3 fx J,cx) dx = (x-4x)J, CX) +2x J,cx)+c (x-4x)J, CX) +2x JoCX) +c

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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: af Let f(x, y, z) = xy + z². Calculate where x = = s², y = 2st, z = t². მs

A: Step 1: Step 2:

Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: Let f (x, y, z) = xyz. Determine the value of fryy + fyay – 2 fyyr Simplify your answers.

A: We have to find the value.

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: Solve the following P.D.E. , with the following conditions: u(0,y) = 0, u(L,y) = 0, u(x,0) = 0 and…

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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: For which value(s) of a and b is y = abx concave up? b>1, a<0 00 0<b<1,a<0 b>1,a>0

A: We have find correct option

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

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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: ∠S and ∠Y congruent or supplementary

A: Given,           To find ∠S and ∠Y congruent or supplementary.

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