2 and y = If x:y:z 4:6:9 and z = 45, then x =

Q: (1) If x²y – xy? + x² + y? = 0, find y' (2) If x² – xy + y? = 3, find y' and y". (3) If x³y – xy3 =…

A: Since you have asked multiple  questions , we will solve the first three questions. If you want to…

Q: 6. Given that z = u' + 2v – x + 3y; u = r´ - s', v = r´ + s´, x = 2rs, y = 4. Find 2 =r dz(r, s, h,…

A: Given, z=u2+2v2-x2+3y2u=r2-s2 v=r2+s2x=2rsy=2rsTo find: dz(r,s,h,k)

Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: If z = x + iy, z/3 – a – ib and * = 2 (a' -b'), then a is equal а b y to

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Q: Let C: |z-il=3 and I = $. , dz. Then e 3z z2 |= 6ti |=0 |= 8Ti |= 4Tti None of these

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Q: 5. By Chain Rule , evaluate a. y' for y = u? + 4u and u = 4x3

A: This question is related to Differentiation, We will solve it using given information.

Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: Find x and y given that (x+yi)/2+i = (1-i)/2+3i

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Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: x then ux is XX If u = V y %3D

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Q: 9(r, t, г) — 5r(7 — сos(t)) — 82

A: We have to do partial differential here.

Q: 1. Suppose W (x, Y, z) = 20z In y – 13x"y3 + 5xz?, (a) Find (b) Find (c) Find OW (d) Find

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Q: : Given a r.v. *=4 3,4,5,then af y= 3x-2, then find ECY), VY) and MCE). Sも), ......

A: Solution

Q: Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

A:

Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

A:

Q: 6) Given that h(x,y) = e**y® _ ¥² Find hxx, hxy, hyy, hyx

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Q: 20. 7 (xx + y), x= st, y=st s= 1, t = 1 %3D %3D

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Q: 10. Find x and y, given that (x² + y²,4) = (25, x).

A: When the Cartesian product is performed between two sets, as a result, an ordered pair is obtained.…

Q: Solve the following aw dw aw. Q1) w(x,y, z) = xy²z³ + esin(x*y²z) + x² – y³ + z – 7 find ( дх ду az

A: Here x,y and z are independent variables and w is the dependent variable that depends on x,y and z

Q: s for :   (x,y)-->(1.5x,1.5y)

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

Q: 1: find af/ox and af/ày.. ) (x, y) = Vx² + y²

A:

Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

A: This question can be solved using the concept of derivatives.

Q: Find when r = 2 and s = 0, if: as z = xy² – x – y x = y = ers 1+s

A: Here given that z=xy2-x-y, x=r1+s,y=ers So, ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s        =y2-1-r(1+s)2+2xy-1ersr

Q: If y=a-5.* and z=a-bs.y , then x is equal to

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Q: 7. w = xe + y in z, Find dw

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Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…

A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To  find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).

Q: 4 - If w = x + 2y + z? , y = r2 + In(s), and z = 2r = X find at the point (r, s) = (-8,4). %3D

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Q: 5. Find aw a. ду дw b. ду at the point (w, x, y, z) = (4, 2, 1, –1) if w = x²y² + yz – z3 and x² +…

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Q: 9. If y = V-|x|, then Dr = %3D %3D

A: Df :  Domain of function f  The set of all input values where f defined

Q: 23 { , si (x, y) # (0,0) b) g(x, y) = 2x2 + y² , si (x, y) = (0, 0)

A:

Q: Show that if x,y∈Z and 3|x^2+y^2 then   3|x or 3|y

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

Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: K (To - T) if 0 <TST. if T, ST y (0) =A

A: Given, dydτ+αy=kτ0-τ , 0≤τ≤τ00             ,τ0≤τ  and y0=A

Q: 3 If U<xy+ yZ +Z X Find d Ce, y,2) y it bcist. V =X +Y+Z, W=)X YZ %3D

A: Given : u= xy + yz +zx , v= x+y+z , w = xyz To find: ∂(x,y,z)∂(u,v,w) Solution: Let   A = u- xy - yz…

Q: 15. In AXYZ, if ZX =ZZ, XY = 13x – 21, YZ = 8x – 6, and XZ = x + 4, find x and the measure of each…

A: given: in ∆XYZ, ∠X≅∠Z XY=13x-21YZ=8x-6XZ=x+4 we have to find x and the measure of each side. that is…

Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: 27. || x sec?y dA, R={(x, y) | 0 < x< 2,0 < y< /4} R 28. || (y + xy-2) dA, R={(x, y) | 0< x < 2, 1 <…

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Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: and u = then the distance from y to Span{u} = line through the origin and y is 2/10. Let y = True…

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Q: 7. If WX= 14 and WR = 8, find RZ. W Y R:

A: We use pythagorus theorem for right triangle to find the side XR and it can be seen that RZ=XR

Q: (b) ƒ(x, y) = Vy – x · In (y+x) -

A: Given (b) f(x,y)=y-x ln (y+x)

Q: 5. If y = In(x + y), find y' at the point (x, y) = (e – 1,1).

A:

Q: Be w =x + 2y + 2°, x = , y = r + In s and z = 2r. Determine and when s = 1 and r = 2 ds Or

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Q: 17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D

A: Let h(x, y, z)=x2+y2+z2-z. We now have ∇f(x, y, z)=(1, 0, 0) and ∇h(x, y, z)=(2x, 2y, 2z-1). Let λ…

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

A: