a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

Q: 1. Use an antiderivative to show that for every contour C extending from a point z₁ to a point 22, 1…

A:

Q: Compute fx + fxy + fyyzz, where f(x, y, z) = z sin(xy)

A: Given f(x,y,z)= z sin(xy)

Q: 7. Let S = [0, 1] × [0, 1] and ƒ: S → R be defined by f(x, y) (2x³+y², 10, Show that f is integrable…

A: Follow the steps.

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A:

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: 3.2= e'-ry ; I=t3 and y = t° %3D

A:

Q: a2 If a;j = aji (ajX;X;) əxyəx; are constant, calculate %3D

A:

Q: 3. Show that the line integral + 2xy) dx + x² dy + 2xz dz, is independent of path in R3, where C…

A: We will find out the required value.

Q: 17. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1, 2, 3).

A:

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

A:

Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

A:

Q: Suppose that z = x/y, where x and y are differentiable functions of u and v such that x = dx/dv 3, у…

A:

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

A:

Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

A:

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

A:

Q: 4. para t> 0, 0 <x < 2 u(0,t) = u(2,t) = 0 u(x,0) = x (2 – x), ди (x,0) = 0

A:

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a…

A:

Q: azz 2. A. If z = sin(3x+2y) , verify that 2 - 3 a2z = -6z ay2 B. If f = x³y³ + 2xcosy + y² lnx then…

A:

Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

A:

Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: and EXPcess du dv as a function of u and v w = Xy + XZ + xz where x = u + v and y = u-v and then…

A: Use this formulas

Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

A:

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: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

A:

Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

A: We have to find the volume by double integration

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

A:

Q: Let f(x, y) = xcosy- y e*y. fxy at (1,0)is equal to:

A: For finding the Partial differentiation we need to take one variable constant and differentiate the…

Q: 10. Para resolver la siguiente ecuación diferencial: y" + 2y' + y = 0 con y(0) = 1; y'(0) = 1 Se ha…

A: The solution of differential equation is given by using Laplace transform and partial fraction…

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: Buuton 5: Expect alion and Varian ce Let X fe a oontinuous pan dom van'able and Y: a X + L you some…

A:

Q: Let f(x, y) = xcosy- y'e*y. fxy at (1,0)is equal to: %3D -2/3 -2 1 0.

A:

Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

A:

Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

A:

Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

A:

Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

A:

Q: Since z = In (x2 + y2), x = eucosv, y = eusinv əz/ðu =? az/dv =?

A:

Q: 2) Find Ow/ôu and ôw/ôv for w= xy+ yz+ xz, x=u+v, y =u –v, z = uv at the point (u, v)= (1/2,1). 3…

A: If w=f(x,y,z) and x=g(u,v) ; y=h(u,v) and z=t(u,v) then, ∂w∂u =∂w∂x.∂x∂u+∂w∂y.∂y∂u+∂w∂z∂z∂u  and…

Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

A:

Q: flz) = Im z is continuous %3D

A: The objective is to check f(z) =Im Z is continuous Or not.

Q: 2. Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xyax - (4y + 2x2)a, + 8zaz. Use…

A:

Q: Let f(x, y, z) = x arctan z. Then solution.] af Əzəy (2,3,1)= a In 2 where a = [Show

A: Find the value of a

Q: What does Peanos EU theorem guarantee for the IVP:  dy/dt = -t/y ,  IC: (to,0)

A: Peanos theorem: "Consider the initial value problem y1= f(t,y), y(t0)=y0. Let f: Domain f →Rn. Then…

Q: that F(x, y, z)= Divergence Theoren

A: The given vector field is Fx,y,z=xz2+12.13, sin y, x·y5. The upper hemisphere can be taken as…