d. VxVy, Q(x + 1,y/2) e. 3xVy3z, P(x,y,z)-4 > 0

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: z = x2 + xy4, x = uv? + w°, y = u + ve" dz when u = 3, v = – 2, w = 0 dv then find:

A: Solve by partial differentiation

Q: (a) f(x,y) = (x² + 1)e" (b) g(w, z) = w? + 22 (c) h(x, y, z) = vT² + 3y – xyz²

A:

Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

A:

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=&lt; 3x2y-z, xz3+y4, -2x3z2 &gt; To Find , grad divV  Let  V=&lt; V1 ,V2 ,V3 &gt; On…

Q: Solve the homogenous differential equation.

A:

Q: 4. Evaluate fo (3x + y)dx + (2y – x)dy along the straight line joining (0, 1) to (2, 5).

A: We need to find the line integral ∫(0,1)(2,5)3x+ydx+2y-xdy .  We first parametrize the line segment…

Q: Calculate fls f(æ, y, z) dS For 2² + y² = 16, 0 < z S ls f(x, y, z) dS =

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: Sx + 2y = 0 xy = -2 (x, y) = ( (smaller x-value) (x, y) = (larger x-value)

A:

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

A:

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

A:

Q: Find Cx(x,y) if Cx(x,y) = 2x2 + 7xy - 9y2 + 4x - 9y - 6 Cx(x,y) = ?

A: Let's find.

Q: Evaluate SS 5ex+y+" dV over B where B = {(x, y, z) : x² + + z² < 1}. Take = 3.

A: The integrals in the form ∭f(x,y,z)dV is called a triple integral. In this problem, we have to…

Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: f(x,y) = x² + 3xy +y² fonksiyonu için fex (2,3)]. [fyy (2,3)] – Fzy (2,3)]? =

A: The answer is, (-5) The detailed solution is as follows below :

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: Ven dy' j + z k B - yi + 4x ĵ + 3²Ê %3D 3. i x (6x マ×(Gx - マ(マ.) - v* つさ

A:

Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

A:

Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: s for :   (x,y)-->(1.5x,1.5y)

A: The given transformation is x,y→ 1.5x,1.5y

Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

A:

Q: f(x, y, z) = 3x + 2y + 4z, x2 + 2y2 + 6z2 = 21

A:

Q: af af a²f 1. Given f(x, y) = x' + y* find ax ' dy' dxdy and - дудх

A: Please see the answer below

Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? Select the correct response: y 2y O -2y O…

A: Topic:- non exact differential equations

Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

A:

Q: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (

A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)

Q: EVawate Fy (Y,y) q Jylx,y) at the indicated point. fir.y)= In (ry) at (-2,-3)

A: Given query is to find the derivative at indicated point.

Q: a) If W =(x,y), where x v²-g' and y 2vg calculate W+ %3D

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: x+2 السؤال الثالث: جد ناتج التكامل (x - 4y + y* z)dydxdzباستخدام التحويل v =, u = 4y – x, W =

A:

Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: (b) / / | /3(x² + y²)dV, where V is bounded by y = 2r² + 2:² and y = 8.

A: The given question seems to be incorrect. The function inside the given square root should be…

Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: 9(x, y, z) = xy + xz + yz; C: r(t) = (1, 21, 3t) , for 0<i54 %3D

A:

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

A:

Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

A:

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

A:

Q: Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

A: follow next step

Q: 3. r/s*t/u- v + w * x - y++

A: Given expression is, rs*tu-v+w*x-y++

Q: f (x, y, z) = xªe²y+æ² zy? – 5zæy³ | af af af dx ' dy' dz Determine

A:

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

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