Date HOMEWORK Given thaqt w = f(x.4,v),y=9 Carviy) and vehca.y) Show that aw - fugy* fyhy +Ju gv hy dy dy 2w 24 2w 22 ay dy dy

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

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Q: GI If U= X+y+Zq V =x+yt ,n'=Yz +ZX +xy grad U.Cgradv x grad w) =o Preve that 11

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Evaluate S. F dr where F(x, y, z) = e'i+ (xe + e²) j+ye²k and C is the line segment from (0, 2, 0)…

A: answer is in next step

Q: Given that w= f (x,u,v),u= g(x, v, y) and v=h(x, y). = f„8, + f,h, + f„g,h, ôy Show that

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Q: (R) Let f(r,y) --In (1+ + y) and u= A- then Duf at (0,0) ia

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Q: az əz If z= f(x,y), where x = (s+1) , y = (s- t). Then Əs at

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Q: If f(x, y) = e + e", then Vf(x, y) = (0, e³). Select one: OTrue OFalse

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Q: E valuate f win Tydy tyxdx olE Cethe line seqment f&Om (0,2) to

A: on solving this we get the

Q: If u = f(y– z, z – x, x – y), then Up + Uy + Uz =

A: u=fy-z, z-x, x-y Let p=y-z, q=z-x and r=x-y. ∂p∂x=0 , ∂q∂x=-1 and ∂r∂x=1 ∂p∂y=1 , ∂q∂y=0 and ∂r∂y=-1…

Q: dz dz Let z= f(x,y) , where x= u? + v? and y= Find and du at (u,v) = (- 40, - 4), given that :…

A: Please see the explanation below

Q: If f(u,v,w)=u+v2sinw  and u=x−y, v=y−z, w=z−x find  fx+fy+fz=?

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Q: A ve B iki küme, f : A → B bir fonksiyon ve X, Y C A olsun. a) f(X) – f(Y) C f(X – Y) olduğunu…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Show Vx Vy[p(x, y) → ¬p(y, x)] E Vx¬p(x, x)

A: Please check the answerin next step

Q: f (x, y, z, u, v, w) 3æyzuvw + x²y²w? – 7cz° + 3yvw Calculate [af af af af af af + for a = y= z = u…

A: Solution

Q: Given f(x, y, z) = /2x? + 5y? + 1z?, find V fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = %3D

A: →Use chain rule of differentiation.→fx(x,y,z) = ∂f(x,y,z∂x . Here, consider y and z as a…

Q: If z = xe, æe then dz = (e )dx + (ryev" )dy. Select one: OTrue OFalse

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Q: Use Gamma Function to evalute the Roll owing 9. e Z dx hint: assume X=2y

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Q: If F (x,y,z) = x²z +elx xy², find (a) V(F + G) and (b) V(FG) at the point (1,0, -2). and G(x,y, z) =…

A: Given Fx,y,z=x2z +eyx      and   Gx,y,z=2 z2y-xy2

Q: dav dyt if va (x*+y*+z) Show that d'v

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Q: 2. Wis subset of V- R3 where %3D a W={(x,y;-1) E IR³ | x, y eR}

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Q: f(x,y,z)=x+y+z and r(u,v)= (2u+ v, 3u - v, u+2v). What is the value of f(r(u,v)) r, xr, AA when u=2,…

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Q: 49. If f(u, v, w) is differentiable and u = x – y, v = y – z, and w = z – x, show that af af ду af…

A: Given f(u,v,w) is differentiable. By chain rule of differentiation , we have

Q: Consider the wff (Vx)[Ey)P(x. v) ^ (Jy)Qx. v)] → (Vx)Ey)[P(x. y) ^ Q(x. v)] a. Find an…

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Q: Given f(z, y) = 6z° – z'y 3y, find f-(z, y) = Preview f,(z, y) =| Preview fa.(z, y) = Preview fay(2,…

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Q: Evaluate F. dr. F(x, y) %3D хі + yi C: r(t) (5t + 1)i + tj, 0 sts1

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Q: f the joint PDF of X,Y and Z is xyz? fx.x.z (x,y, z) = 0<x<1,0< y < 2,0 < z < 3 9. 0, otherwise

A: Solution

Q: 14. We know that S(x,y)dx+g(x,y)dy] = Se f(x,y)dx + Se g(x, y)dy. Use this knowledge to evaluate S.y…

A: We integrate this by making two path where for one path only y vary and for other path only x vary.

Q: Given f(z, y) = =* y – z'f, show that fry = fyx-

A: See the attachment

Q: Find the extrema of the function u, if obtain on the set M. Thank you.

A: The maxima of a function in a constraint can be calculated using Lagrange's multiplier method. The…

Q: Q/ If the joint p.d.fof X and Y as f(x,y) = }*y (cx?y ,x2sys1 ,0. W find the value of c and P(x 2…

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Q: a) f(x,y) = xcos(V) + ye*

A: We apply first and second derivative over function

Q: Find fayr. f(x, y, z) = r*y"s* + xy' + y°z

A: The given function f(x,y,z)=x3y5z8+xy9+y3z

Q: (2wv – tan w) du + (v² - v sec? w) dw = 0 %3D C = yv+w tan v Option 3 O None of the choices C = yv –…

A: Given differential equation is solve by exact method

Q: compule the W a M the veter field the perametenísed jind ni t yÏ and s is orientked doeunward o…

A: Now, we have to calculate the parts of integral and then put it in the integration.

Q: Practice by Evaluating So Fodr where, F (x, y, z) = xyi + xzj + yzk C :r (t) = ti + tj+ 2tk, 0 < t…

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Q: Let f(x, y) = y cos (xy), then f.(x, y) = fy(x, y).

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Q: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: The domain of f(x,y) = In ry is points (x, y) in the first quadrant. Select one: O True O False

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Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

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Q: Given f(x, y) = 3x° cos (y"), find f-(r, y) = fy(x, y) = fae (x, y) = fyz (x, y) =

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Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: дхдуда dydzdx dzdxdy

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Q: arametrize the monkey saddle z=x^3−3xy^2 by using u=x,v=y as the parameters.  plot the image

A: Given equation is, z=x3-3xy2 Take u=x,v=y Then the equation becomes, z=u3-3uv2 The counter map is,

Q: Let f: X Y and suppose S, {A;}ieI C P(X) and T, {B;}jeJ c P(Y). Show that cn. iel (i) f

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Q: let f(x, y, z) = 2x?y + 3xyz-x z+3y Find: fx . fxy, frz fryz

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Q: z = x + xy, x= uv + w, y= u + veW dz az az when u = 1, v = 1, w = 0 du dv dw dz %3D du dz %3D dv dz…

A: We have given  z = x4 + x y3 , x = u v3 + w4, y = u + v ew To Find: ∂z∂u, ∂z∂v, ∂z∂w when u = 1, v…

Q: Evaluate fy and f, at the given point. f(x, y) = e³Y sin(x), (T, 0) fx(T, 0) fy(T, 0) %3D

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Q: If w ry + yz + . I=u+v. y=u-. and z=uv find at the point (u, v) = (; .1). ) None of them b O d. e f…

A: Given: W=xy+yz+zxx=u+vy=u-vz=uvfind∂w∂v at(u,v)=12,1

Q: az au əz əv əz ?w 11 11 || z = x² + xy³, əz əz du av az aw x = uv³ + w², y = u + vew when u = 1, V =…

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Q: If || f(t, y) dA > 0, then f(x, y) > 0 for al D (x, y) in D.

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