f(x, y, z) = 3x - 2y + z- 12 = 0 g(x, y,z) = 4x + 2y - 25 = 0 h(x,y, z) = x- y²z-7= 0

Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: An image is projected onto a wall, and the irradiance of the light on the wall is (3) given by f(x,…

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Q: (a) Find the critical point of f(x, y) = (4x? – y) (x2 + 4y). (x, y) (0,0) (b) Find the…

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Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: ation. 4x y"-5y' +3y = 0 around xo = 2 x) = a, (1 -- 2* + 103 1536 Ob. 11 103 y(2) = a, (1+*- 2) .…

A: Given that, 4x2y''-5y'+3y=0 The x2 can be rewritten as, x2=(x-2+2)2 =(x-2)2+4(x-2)+4 So the equation…

Q: One of the critical points of the function z = f(x,y) = 4x -12xy+ y +1 is (0,0,1). [Notice that I !!…

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Q: Find the orthogonal trajectories for the family of curves (enter your solution as an equation)…

A: Nothing

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: 3. Find the derivative of the function f(x, y, z) = xy³ + yz³ + zx³ at the point (-1, 2, 1) in the…

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Q: Find the critical numbers of the function. g(y) = g(y) =  y − 2 y2 − 2y + 4

A: the given function is: gy=y-2y2-2y+4 we have to find the critical numbers of the given function.

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: Find the partial derivativef,for the functionf(x,y) - &x+y. 1,(x.y)- 17 1,(x.y) = Sx+y Sx ,(1.y) =…

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Q: e critical point of the function f(, y) - 6 +7x + æ² + 4y – 2y?

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Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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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: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

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: g(x, y) = 6x² – 3y², (/8, /5) Gradient is f(r, y) = tan 6y (16, 2) Gradient is

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Q: The partial derivative of a function of two variables are represented by f,(x,y) which is the…

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Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: A line I has a gradient of m₁ = Which one of the following lines will intersect I at right angles? 4…

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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: The demand for a car wash is x = 1000 – 40p, where the current price is $3. Find the price…

A: Consider the given information. x=1000-40p The current price is $3. Rewrite the function in form of…

Q: (a) Find the critical point of f(r, y) = (4x² – 3) (2² + 43y). (x, y) (b) Find the discriminant,…

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Q: The productivity of a certain country with the utilization of x units of labor and y units of…

A: It is given that,  f(x,y)=100x0.72y0.28

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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

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Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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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: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 3x? -…

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Q: )The value of partial derivative f-(1,-1,2) of the function f(x, y, 2) - x - Vy2 + z? is: %3D

A: Given function f(x,y,z)=x-y2+z2

Q: For demand function 2 = a-bP and supply function Q, = dP-c , using Cramer's rule determir..…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: Consider a competitive market in which price adjusts to excess demand or supply and firms enter and…

A: given that                                                 dpdt=0.5qD-qs where qD is demand…

Q: dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt

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Q: Find the partial derivatives of the function 3z - 8y f(r, y) -9z + 8y fz(x, y) fy(z, y)

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Q: The function f (x, y) = x³ + y³ + 3x² - 3y² - 8 has local minimum at the critical point (0, 2). True…

A: To tell if the given statement is true or false.

Q: Find the orthogonal trajectories of a system. x'y2- 2xya + a2 0 %3D

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Q: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

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Q: The temperature T(x, y, z) is given by T(x,y,z) = 4x2 − y2+ 16z2. In which direction T increases…

A: We have to find the maximum rate and the the direction where T increase

Q: t3 – 1– 2vt - f(t) = -t5 2 f'(t) : t3 5 %3D Vt11 t6 2t3 – 5 – 9VE f'(t) = t6 7t3 – 9VE f'(t) t6 9 5…

A: f(t)=t3-1-2t-t5

Q: ind the orthogonal trajectories of x^3=3(y-c)

A: Given equation of curve  is   x3 = 3(y-c)  we have to find  the orthogonal  trajectories

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

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