2- Obtain the function x to minimize the following functional. = [ c«f + *)dt J = St: x1 = -X2 , x(0)=fixed x(1)=fixed %3D

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

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Q: equilibrium

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Q: Solve the given optimization problem by using substitution. Minimize S = xy+xz + yz subject to xyz =…

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Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: compute the first-order partial derivatives. z = ln(x2 + y2)

A: Consider the given function z=lnx2+y2 We have to find the first-order partial derivative. ∂z∂x, ∂z∂y…

Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: (b) Compute the partial derivative fy at the point (x, y) = (1, 1), or show that it does not exist.…

A: Let f:R2→R  be the function   F(x,y)=x-1.y-113(b) compute the partial derivative fy at the point…

Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

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Q: Find the approximate solution of the Poisson equation uxx + Uvy = -1, x| < 1, ly| < 1 u = 0 at x =…

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Q: 1.Test the function def ined by f(x.y)=xlnx- ylnx for its homogeneity. If it is homogeneous, give…

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Q: 12.) Compute the first partial derivatives of the following function. f(x,y) = 2- tan 1 (7x² + 2y²)…

A: The given function isf(x, y) =2tan-17x2+2y2to find partial derivative fx, fy

Q: If f (x, y) is a homogeneous function of degree n in x and y and has continuous first and second…

A: This question is based on Euler's theorem statement.

Q: Find all the second partial derivatives of the function a) f(x,y) = x* – 3x²y³. %3D | b) f(x,y) =…

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Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: to Find the first partial derivatives of g(x,z) = x In (z dg dx ag dz

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Q: Compute the indicated partial derivative. g(x, y, z) = x³y^z° 9xxyz =

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Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: Find the first partial derivatives of the function. w = In(x + 3y + 6z) 3 %3D ду x + 3y + 2z aw dz…

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: Calculate the second-order partial derivative of f(x,y) =sin(x³y²) with respect to x and y, that is,…

A: given f ( x1 y) =sin ( x3 y2)   ∂2f∂x∂y=∂∂x∂f∂y

Q: Compute the given partial derivative. f(x, y) = 8 sin(4x² – y), (0, 1) f,(0, 1) = %3D

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Q: 1. u= x² + y² + z²

A: On solving this we will get

Q: If f is a function of x and y such that fxy and fyx are continuous, what is the relationship between…

A: Function: fx and fy are continuous function. Let us choose f(x,y)=x3y3+πxy Here fx=3x2y3+πy…

Q: 3. Construct a suitable Liaponov function of the form ax + by and use it to determine the type of…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: Solve the given optimization problem by using substitution. Minimize S- xy + xz + yz subject to xyz…

A: S=xy+xz+yz  =xyzz+xyzy+xyzx

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: Find the first partial derivatives of the function. z = (4x + 3y)4 Əz ax az ay %3D I.

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Q: Find the first partial derivatives of the function. z = (8x + 7y)5 Əz ax az %3D Əy

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Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2

Q: If f(x, y, z) = 2 sin(100xy) In(2), compute the value of the limit f(1, h, e) – f(1,0, e) lim h→0 h

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Q: A certain function f(x,y), which has continuous second-order partial derivatives on R2 , has (0,0)…

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Q: 1)Consider the function f(x, y) = x° + 2xy + y? – 5x b) Calculate the second-order partial…

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Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

Q: Find all the first order partial derivatives for the following function. f(x, y, 2) %3 2(e Х) У af…

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Q: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: 1. z=x - xy + 3y ?

A: Given: z = x3-xy2+3y2 To find: The first partial derivatives of the given function.

Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

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Q: Find the second order partial derivatives дхду of and дудх f(x,y)= 4x² + In x + e*** – cosy +9y +3.

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Q: (xy(x² – y²) f(x,y) ={ x² +y² si x² + y² + 0 0 si (x, y) = (0,0)

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: 8. Find the orthogonal trajectories of y cx

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Q: If z = f (x, y) is a function that admits second continuous partial derivatives such that ∇f (x, y)…

A: