дw дw find if w w %3D 2x* + 3y аnd ds 'ðu х3D 2 su3 y = 5e-3su

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: To convert the nonlinear DE xy²y' = y³ – x³ to become a linear DE we use the substitution y= u"…

A: Given the nonlinear DE  xy2y' = y3-x3

Q: J = fc cosh (z) dz, z2-3iz C: |z| = 1

A:

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

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

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

Q: If W = 2x3 + 3y², a 5t2, y = 2t³ %3D = %3D dW then find at t= 1 dt O 1912 O None O 1273 O 1572 2212

A: A detailed solution is given below

Q: iv) if zx = (y)¯1 then zx/Zy %3D

A: We have to find          zxzy where , zx=(y)-1 If ,   z=z(x,y)  then,∂z∂x= derivative of z with…

Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: Suppose w = 6xy + In(4 + z²) , x = - , Y 3u + 9v, z = cos(8u). Find dw/dv when u = -5, v = -6. dv…

A: *to find:- Partial derivative of w with respect to v, when u = -5 & v = -6

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

A:

Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: Solve the following first-order linear DE's. a) y' + 2y = x³e-2x b) y sin2x 7 +: y c) x²y' +3y = x?

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Q: 2.rydr + (z² – 1) dy = 0 O zy? - y = C O zy+y=C O zy - y² + C = 0 Oy-

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: d the values of az/ax and öz/ay at the point z - xy + yz + y' - 2 = 0, (1, 1, 1)

A: Given that  z^3-xy+yz+y^3-2=0 To find the partial derivatives at point (1,1,1)

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

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Q: If x= 2u3 – 3u² and y=u³ – 3u, then dy is dx u+1 (A 2u u+1 B и — 1 2u и — 1 D

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Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

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Q: 2. W =I+xy- Z finds Wzz WZX NJ 3.

A: Given W = 1 + xy2 - z2

Q: 5. Find the particular solution of D' + 3D° + 2D° ]y=0 provided that when x = 0, y = 0, y' = 4, y" =…

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

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Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

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Q: If f(x,y) = 3e2y cos (x-2), then the linear approximation at (2,0) is %3D (A) 3-3x (B) 3+ 6y (C)…

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Q: 1. Evaluate ff. y dS where S is the portion of the cylinder 4x2 + 2y2 = 16 that lies between z = 0…

A: Since you have asked for a question with multiple sub-parts, we will solve the first question for…

Q: y'' + 7y'+10y = 0, y(0)=-4, y'(0)=2 BDP nin genel çözümünü bulunuz.

A: Given differential equation is y''+7y'+10y=0......1 and y0=−4, y'0=2. We have to find the solution…

Q: B = {(x,y xs2, -a sy s3, 0£21} SS, x*yz²dV 2 'B

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: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: If f(x, y) = 3e-2x cos (y – 2), then the linear approximation at (0, 2) is (A) 3 – 3x (B) 3+ 6y (C)…

A: A function of 2 variables can be linearized using the partial derivatives. The formula for the…

Q: 3. Let x? + y² + z² = ? 3ryz, then which of the following is %3D 2y–3zy O a. 2z-3zy 3zy–2y O b.…

A: Note that, here x and y are independent variables and z is the dependent variable. So, we will apply…

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

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Q: 3- prove that w comport dx =w dy yx 23 34 if w=: w = xy² + x³y² + x³y

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Q: 8. If JM = x + 17 and MK = 5x – 23, find JL. %3D H. 'K

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: 11, If PQ = OR, JK = 3x + 23 and LM = 9x- 19, find PK. %3D %3D %3D K J R. %S'

A:

Q: What is P-(y) if the given DE is xydx – (3y – x²)dy = 0? -2y 2y 2 y -2y-1

A: Given : Linear differential equation  Need re write in x form as follows dx/dy +P(y)x=Q(y)

Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (a) z = x2 - 2y2 ; x = 3s + 2t, y = 3s - 2t

A: It is given that,            z = x2-2y2  ;  x = 3s+2t  ;   y = 3s-2t We have to find  ∂z∂s  and…

Q: If V=3x^2i+4yj+k andl=ti+t^2j+t^3 k.Finds V. dl wherea=(0,0,0) and b = (1,1,1). 山

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Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

A:

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: IfA = ze2xVi+2xycosy j+ (x +2y) k then the valueof Vx A at the point (2,0,3) is Select one: a.…

A:

Q: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

A:

Q: Hew.3Findwandow de when P=ty9-4if: be W = xy +yZ + Zu +uV and x = Pg ,y=4 tan P 2= Ln L4-3e) V =P++1

A: put value of x,y,z,u,v in w to solve the partial derivative.

Q: 4. and A= Find flA) where f lt) = t"-2t+3t+ 3t +2 て %3D %3D て

A: Given,  A=124-1 f(t)=t4-2t3+3t2+3t+2 Find: f(A)

Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

A:

Q: Find the solution of BVP 2. Uxy = 4xy+ex ; uy (0,y) = y, u(x,0) = 2

A: uxy=4xy+ex uy0 ,y =y u(x,0) = 2 To find solution of given differential equation