(a) Given w(x,y, z) = 2xyz,x = s² + t²,y =,and z = Int, find - and Ss Sw

Q: Let f (L, K ) = 32LK. Find df/dL.

A: Differentiate the function f with respect to L.

Q: Find paromet ric aquation of Line L where to paiut A(Xmiya) is and

A:

Q: Find dy y = e fin (52) for り =

A:

Q: 耳 ixn=wyr Show that d P

A: Given a function is two variables.

Q: dy a) Find in terms of y, if x= e* in terms of y, if x= e*+Insin y dx

A:

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

A:

Q: y A. A' B' 6 54 123 4 5 6 2 C

A: given diagram is

Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

A:

Q: If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

A:

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: a = -2, b=2 u=x, and dv =e*dx • Then: udv =

A: From the integral by parts formula, ∫udv=uv-∫vdu As, u = x, dv = exdx, then v = ex , also if  u = x…

Q: SiSi dx dy dz Q4) Evaluate xyz

A:

Q: Sx³Vx2 + 12 dt

A: We have to evaluate the integral: ∫x3x2+12dx In this case we will use substitution method  let…

Q: Let r(t) = (cost,sin t, ln(cost)).Find T, N, and B at (1, 0, 0).

A: Let rt=cos t, sin t, lncos t at 1,0,0 Find T, N and B. Tangent vector to the curve is denoted by…

Q: If u = 2-x, x/2-xd

A:

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: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

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: 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: 2л where a, b > 0. dx = - ile* + b Prove that %3D

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Q: = 10. The triple integral dxdydz:

A: Here we have to evaluate the given triple integral.

Q: For f(x, y) = xe**Y, find fy (1, In 2) O 2 O 2 In 2 O 4 In 2 +2

A: