fx (x, y)=-2xety-x²-y- fxx (x, y)=-2e4y¬x²-y² + 4x²e4y¬x²¬y? fy (x, y)=(4 – 2y)e+y¬x²-y² fyy (x, y)=-8ye4y-r²-y* _ 2e+y=x²-y² + 4y²e+y=x²- + 4y²e%v=x²-

Q: y= cosV1- x y' = V1-x² ² y' = 2v1- x² y' = 2va- x2 y' = Vx-x* 1 y' = 2Vx-x2

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Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: (ux – u² – x²) dt max subject to х %3D х + и, х(1) 3 2.

A: As per the question we are given a optimization problem, and we will find the optimal control law by…

Q: 2y" +2y=2sinx y(0)=0, y'(0)=1

A: Solution y=CI+PI CI=Characterstic integral PI=Particular Integral P.I=sin xD2+1Let D2=-α2so…

Q: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

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Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

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Q: 1 5earctan(y) dy -1//3 1+ y2 3 1+ у2

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Q: If IAIo the equilibrium paintx=0 for the system x-Ax isa stable focus

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Q: Find the critical points of f (x, y) = 9y + x² + xy – 5y - y'.

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Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: f(x, y, z) = eVx2 + y2, E = {(x, y, z) | 1 < x² + y2 < 4, ys 0, x < y/3, 3 s z 5 4} E = {(x, y, z) |…

A: given fx,y,z=ex2+y2 and a region of integration E=x,y,z|1≤x2+y2≤4 , y≤0, x≤y3 , 3≤z≤4 claim-…

Q: a Find all critical points of z = (y- 3)(z+ 2y+ 7), = (y+z). Show work.

A: We have to find the critical points of the given equations. For the critical points find the…

Q: dy 1 dx 3y3 By the method of separating the variables y = x3 y = Vx+ c Option 1 Option 2 y = vx + c…

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Q: (b) x' = -x – 3y + 2z + yz, y' = 3x – y – z + xz, z' = -2x + y – z + xy.

A: As per your query the solution of the part (b) has been done in detail in the following steps.

Q: Compute (T2 T)(x, y). T(x, y) (3x, 7y), T2(x, y) = (x-y, x + y)

A: We have to find T2 composition T1 .

Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

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Q: Vx2 +1 – Vx² – 1 y = Vx² +1+ vx² – 1 2.x3 dy = 2x - d.x - - show that Vx4 – 1 -

A: Given: y=x2+1-x2-1x2+1+x2-1      ......(1) To Prove:  dydx=2x-2x3x4-1      ......(2)

Q: linearize the nonlinear equation in the region defined by 4 < x < 5, 3 < y < 4 z = y?Vx + 5e(3x-y²)

A: Given, z=y2x+5e3x-y2 The goal is to linearize the given equation around the operating point,…

Q: (2) Find dt2 if y = x2 + 3x -7 and x 2t + 1 | 2

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

Q: V2x-x2 SS2*-*" (x² + y²) dydx

A: Changing cartesian to polar coordinates: x2+y2=r2x=rcos θy= rsin θ x ranges from 0 to 2y ranges from…

Q: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = -3x2y3 + x3y

A: Given that, fx,y=-3x2y3+x3y Then we get,…

Q: The function f (x, y, z) (3, 0, 0), (0, 2,0), (0,0, 6) and (1, , 2) What is the value of a? = xyz…

A: To find the critical points of the function f(x,y,z), subject to the the constraint g(x,y,z), apply…

Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

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Q: Maximize F=x+y subject to:  x+2y≤8  x≤6  x, y ≥0 Corner points at ____________________ Maximum…

A: We have to find maximum.

Q: Find L(y). y +2x = 2 Y – x' = et y (0) = x (0) = 0 %3D %3D -2 L (y) = %3D s(s²+2) 1 O L(y) = (s2+1)…

A: Given; y'+2x=2 y-x'=et y(0)=x(0)=0.

Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

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: y'+2y/x=x, y(1)=2, y(2) using h=0.1

A: given :y'+2yx=xy(1)=2, y(2) using h=0.1

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: From the given information the given curves from which the volume is to be generated are:

Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

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Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

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Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

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Q: 2y + z = 1 29. у + 2z 3D 5 y (x + y + 3z = 8

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Q: = 3(2x + y)² + 1 2x + Y = y=1 = vY

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Q: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: (18) y "+9y '= sec² 2x %3D (19) y "'+6y "–14y'–104y = -11 le*

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Q: 4y² –7y–12 – , dy + y3-y2-6y dy + dy + dy 5(у-3) 9 5(у+2)

A: Given: ∫124y2-7y-12y3-y2-6ydy=∫1295y+2+2ydy+15y-3dy To find the solution. Solution: We have given,…

Q: find the first and second derivatives. 1. y = -x2 + 3                                2. y = x2 + x +…

A: 1) Given thaty = -x2 + 3On differentiating y with respect to x,

Q: dy 3y y torh(x) + 2

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Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: 2x y'' – 3y' – 10y = 7e y(0) = 1, y'(0) = - 17 - %3D %3D

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Q: 2X + y - x - 2y + 2z = -11 3x - y + z = (x, y, z) =

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Q: برهن على صحة التكاملات التالية : fx²J, (x) dx = x²3, (X) + x1(x)-[Jux) dx J, [x*J₁ (x) dx = x* J,…

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Q: 10. Find and Classify all critical points of flx,y)=-x + Xy +3y-Sx-Ay +2. 2 for

A: Let us consider two variable function z=f(x,y) To find the maxima and minima  Find the first order…

Q: 3y - t2 dy = 0; y(1) = 1 + y5 dt' 2y4 O t? = y°(3- 2y2) O t3 = y(4- 3y?) O t? = y(7-6y?) O t2 = y²(6…

A: Solve the initial problem:3y2-t2y5dydt+t2y4=0; and y1=1.

Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

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Q: d2x/dt2 + 4 dx/dt + 3x = 2 x(0) = x’(0) = 0

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