82z 82z + 8x2 82z If z = x + y lnxy, show that x- = y², y2. 8y2 ID 8x8y

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

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Q: The productivity of a country is given by ​f(x,y)=14.41x0.427y0.573​, where x is the amount of…

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Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: f(z) = 4z and g(z) = 8z² . e them by comma)

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Q: 1 dz (z + 1)°(2:² + 4z – 34)i

A: Solve, as follows:

Q: 4.3 Verify that for f(x, y) = 4x°y$ - 9x*y³. дх ду ду дх df

A: Explanation of the answer is as follows

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

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Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

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Q: %3D %3D = 7 and y = 7, find z when x = 3 and y = 5. Round your answer to two decimal places if…

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Q: 1. Find x, y, and z so that x + y 4x 2y -16 -- y 11 4 Z

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Q: Мaximize z 3 2х + у За + 4у < 36 6x + 2y < 36 Subject to Маximum is at y = VI VI ЛІ ЛІ II

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Q: dx 7. JIVa² – 2x + 5 (hint: let æ² – 2x + 5 = (z – x)²) -

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

Q: Q2 Given that z = 8x2y - 2x + 3y, x = u v, y = u – v %3D az az and ди Find av

A: To find dz/du and dz/dv.

Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: Y1 (t) = 2t – 3, y2(t) = t² + 1, y3 = 2t² – t, y4 = t² +t +1 %3D

A: We will find out the required solution.

Q: Solve ylk + 2) + 2yjk + 1} + v[k] = 0 if y[-1] = 1, y[–2] = 1 %3D

A: Given,                            y[k+2]+2y[k+1]+y[k]=0                               ...(1)…

Q: True or False. Justify. dz → 0 as R → ∞. 2z3 + 4 ||zl=R

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Q: f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

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Q: S(2y + 3)?/ y+ 2 dy

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Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

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Q: the of olution using simplex me Max z = 8x, + 10x, + 7x3 s.t: 4x + 6x3 + 3x3 S 60 7x, + 2xz + 5x, S…

A: In this question, the concept of Linear Programming is applied. Simplex Method An approach to…

Q: Lion 1-y If x = Show that 1+y dy V1-y

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Q: af Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x + 1)? Select the correct answer below: O In (3z² + 4æ +…

A: Given, rx=lnx3+2x2+3x+1

Q: 2. Find deri vative y T-2X y=3e6x %3D

A: Given,          y=3e6x+e1-2x

Q: a2z + əx2 a²z If z = In(x? + y²), find ду?

A: Find ∂2z∂x2+∂2z∂y2.

Q: y''+6y=6+x By using i) Method of undetermined coefficients ii) Method of variation of parameters…

A: i) Given that y''+6y=6+x Take m=ddx m2+6=0m2=-6m=i6 Hence the homogenous solution is…

Q: واجبات اوجد الكل م ما ياني o y = 2t2 + 1, t 5x r2 + 1 y = r = 6x O y = V2u, u = 2Vx

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Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: Q.1) Evaluate, (a) 3y In (y) dy 7+1 zp- (ь)

A: Find the integral

Q: Мaximize p = 10x + 10y + 15z subject to + z s 12 X y - 2x 2y + z 2 14 -y + z 2 4 x 2 0, y 2 0, z 2…

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: ų (H)= - 2y, (t) + 24;(4)= Y,(4) - 2y, (t) +2t t 9,lFS +2

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Q: 190.19 b.) 6Xi t 15X2-24 y3 f 40x4 > 69.8 ¥3 15X, + 9x2 -13 V3 -24Y1 参3X t18 y3- 1 Xy = -163 " xy=…

A: Here we use a = x1 b = x2 c = x3 d = x4

Q: Find curl (8z i + 9x j + 10y k). curl(8z i + 9x j+ 10y k) Di +(i Dj +( )k

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Q: exy2z 1. Given Vx²y + y²z+10=0. Find 2. yz

A: Explanation of the answer is as follows

Q: Find curl (7z i + 8xj+ 6y k). curl (7z i + 8x j + 6y k) = ( Di + ( j+ ( )k

A: We have to find curl7z i +8x j+ 6y k Now,  curlP i +Q j+R k=ijk∂∂x∂∂y∂∂zPQR

Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: 1. V2 3y 8-x2-y2 رار 0 0 x2+3y2 dzdxdy

A: We have to evaluate the integral.     According to our guidelines we can solve only one question so…

Q: 33) - 2y + y, + y; = 0, y + y', = 4t +2, y, (0) = y, (0) = y,(0) = 0 y + y, = t² +2

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Q: 7. x + 3y + 522 = 173.61, x - 27y + 2z = 71.31, 41x - 2y + 3z = 65.46. Start with x = 1, y = - 1, z…

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Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & Z then simplify.

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Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: 87 V 174x-x2 9Vx2+y2 dydx = %3D

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Q: 6 4 for f(x, y) 3 3x у - 4x'у". 5 3 Verify that дх ду ду дх df 4 5 18y x - 20y°x of 5 3 4. 2 18x°y -…

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