If f(x, y, z) = In(x° + yº + 2®) + v(x° + y8 + z®), then find f, fy and f; at (1,1, 1). %3D

Q: Let f (x, y) = 3x2 + 2xy + 5y. (a) Calculate df/dx (1, 4). (b) Evaluate df/dy at (x, y) = (1, 4).

A: Differentiate the function f with respect to x treating y as a constant to calculate ∂f∂x.

Q: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

A:

Q: f(x, y, z) . The total differentia %3D by o af Aæ + af Ay + az fe -Az df o df df · Ay + dz Az Ax +…

A: Given that: w=f(x, y, z)

Q: The function f (x,y) = e* +3 tan – is a homogeneous function of degree_

A:

Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

A:

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

A:

Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (r, y, z) = sin 2x i + xz cos y j+ e*y iv F,

A:

Q: (A) Find div (e grad u xf) at (2,1,0) where x-y and =(x²+1)i+sec¯¹(x² −y)j + 3y²z. k YZ 11=

A: What is grad, div and curl: Gradient, divergence and curl are important in vector calculus. Gradient…

Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? %3D Select the correct response:

A:

Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

A:

Q: dz Use chain rule to find at (u, v) = (1, 1) if dv z = z sin(y² – z + 1)4), e = 3u – v², y = vº.

A:

Q: Suppose X and Y has a joint pdf given by f(x, y) = 6x, 0 < x < y < 1, and zero otherwise (a) Find…

A:

Q: Find the bounded solution of âyở y x> 0, t>0 where y (0, t) = 1, y (x, 0) = 0.

A:

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

A:

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

A:

Q: Integrate G(x, y, z) = z2, over the hemisphere x2 + y2 + z2 = a2, z&gt;=0.

A:

Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

A:

Q: Find Vf at the given point. f(x,y,z) = x3 + y2 – 3z2 +z In x, (1,2,4) Vil(1,2,4) =Di+j + ()k ( %3D

A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: f (x, y) = xlx - alny is %3D O homogeneous 0 degree O not homogeneous O homogeneous 2nd degree O…

A:

Q: Find f, fy, and f. f (r, y, z) = z In (a*y® cos(2z)) f%3= fy = %3D fz =

A:

Q: dw Find where w(x, y, z) = xyz + xy, with x(t) = e", y(t) = e¯24 and z(t) = e-9t dt

A:

Q: Vif the joint pdf of the RV (X, Y) is given by f(x, y) 1 exp {- (x² + y²)/2 o}, – ∞ < x, y < oo,…

A:

Q: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).

A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)

Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: Find fæ, fy, and fz. f(z, y, z) = z In(a"y cos(5z) 4.3 = z In (x*y° cos(52)) fr = fy = f: =

A:

Q: (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x + y = 0). (j) (Væ…

A: .

Q: The joint PDF of X and Y is 5y -1< x< 1, x² < y<1 fx,y(x, y) = 4 otherwise, %3D Find E(VY).

A:

Q: dz at (u, v) = (1,1) if du Use chain rule to find -z + 1);), = x = 3u – v², y = u® z = x sin( (y? |…

A: If the input of the function is more than one, then it is called a multivariable function. In this…

Q: Given that f(z) = y – x – 3x²i. Find S f(z)dz OB B-1+i A=i

A:

Q: dz Find given: dt z = xe", x = tº, y = 1+ 4t

A: Given,          z=xe3y , x=t6 , y=1+4t

Q: Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

A:

Q: If f (x, y) = 4e4*cos (y - 1) , then the linear approximation at (0, 1) is %3D (A) 4+ 16x (B) 4+4x…

A:

Q: d) Find for w = xy + yz + xz , x = u + v , y = u – v , z = uv dv %3D at the point (u, v) = (-2,3).…

A: Given, The  functions  W=xy + yz + xzx=u+v,y=u-v,z=uv and the point is (u, v) = (-2, 3).

Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: dy + ydx %3D = 3x²y?dx,

A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

A:

Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: The function f (x,y) =e" + 3tan an( y/x) is homogeneous of degree А) 3 в) 2 cC) 1 D) 0

A:

Q: Find (∂ w/∂ x)y, z if w = x2 + y - z + sin t and x + y = t.

A: To find the partial derivatives.

Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32…

A:

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation