f(x, y) = 3x² f(x + Aх, у) — f(x, у) f(x, у + Ду) — f(x, у) (b) (а) Ax Ду

Q: f (x, y) = 3x²: f (x, y) = x² + 3y²: f (x, y) = y – 2x?: f (x, y) = 5x² – 5y²:

A: The function f(x,y)=3x2  Level curves are made by fixing values of fx,y=k.…

Q: find div(F x G) = V • (F x G). %3D

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Q: f(z) = (x²+y)+i(y²-x) is analytic

A: Let  fz=fx,yu+iv=x+iy the function must be continuous and differentiable at all points in it's…

Q: Use chain Rule to find for 2. y = . +x²+x+1 I.W | 3. y = estn 3x Н.W

A: We have to find dydx using chain rule for the given function: 2.  y=1x3+x2+x+13.  y=esin 3x We know…

Q: 22) About the x-axis y = 5 x =V25 - y2 X =' + 3 4 5 х 2. 3. 2.

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Q: Approximate V(2.03)² + (0.8)² + (2.1)² using a linear approximation.

A: To approximate: 2.032+0.82+2.12 Consider a function, fx,y,z=x2+y2+z2 The linear approximation of a…

Q: f(x,y)=x² +y° +3xr² – 3y² –8

A: Given f(x,y)=x3+y3+3x2-3y2-8To find critical points, we first compute∂f∂x and ∂f∂y  ,…

Q: How can linear approximation be used to approximate the change in y = f(x) given a change in x? To…

A: From the formula of first derivative f'(a)=f(a+h)-f(a)h       =f(a+△x)-f(a)△x, h=△x

Q: f(x,y) = x² + 3y² + +xy b. f(x,y) = /x² + y² a. %3D

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Q: f (x, y) = 169 x² + y² at (-3,2).

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Q: Use the linear approximation of f(x) = /2x - 3 about c = 2 to estimate the value of V1.32 Enter your…

A: Given that: f(x)=2x-3

Q: function 3y + 1 + y = 0, is: %3D

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Q: F=(x-y², x²•y +3) at A-(1, 1), B=(2, –1) and C=(0,-2). %3D

A: The divergence of a vector field F = <P,Q> is defined as the partial derivative of P with…

Q: Find the linearization L(x,y) of the function at each point. f(x.y) = x² + y? + 1 а. (2,1) b. (0,2)…

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Q: f(x, y) = 1 + x2 - y2 R = {(x, y): x2 + y2 < 1}

A: Find the area of surface given by z= f(x,y) that lies above the region R.

Q: f (x, y) = x+ 5y 2 +y = 25,

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Q: f(x, y)=√x² + y², y = 1², x = t

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Q: (t + 2)°y" + 3(t + 2)y' +y= 0, 1>-2, V1 = (t+ 2)

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Q: f(x, y) = x²/(1 + y²) (a) f(-5, 0) (b) f(14, 1) (-) (c) | (d) f(-8, y)

A: Put value of x and y in given equation.

Q: 1. Let f(x, y) = 8x³ + y³. Find fæ(0,0). %3D

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Q: Use method of variation of parameters. y" +2y-8y = 2e-2x - e-x.

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Q: Let f(z) = 5z2 + 3z. %3D

A: Given,            f(z)=5z2+3z and         z = 8.2+5.9i

Q: 4. Sketch: (a) f(x, y) = 4 – x² – y? f (x, y) = x² – y² + 2x ** (b) (c) f(x, y) = /A– x² – 4y² f (x,…

A: 4. (a) We are to sketch the graph of the function f(x,y)=4-x2-y2 \

Q: The domain of y = v2 – x is A. (-0,2] B. (-0,00) C. (-∞,2) D. [2,0) E. 0

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Q: 13. y = 5 – Væ, x = 1, x = 4 and the x-axis.

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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: mence Jove Q 6. Find the orthogonal trajectories of the functiony = x + ce-, which is passing…

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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: Determine the parameter of y+f(x)y=g(x) A

A: Given that, y'+f(x)y=g(x) The solution for the equation of the form y'+p(x)y=q(x)…

Q: Find (i) fx (x) (ii) fy V) (iii) are X & Y indepdent? (iv) f, (x/y) (v) (y/x).

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Q: Find fxy(x,y) if f(x,y) = (x² + y²)6.

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Q: Determine the linear approximation of f(x) = x° at x = 1. a. y= 8x +7 b. y=- 8 x - 7 C. Not in the…

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Q: f(x,y) = x +y +8x- 2y

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Q: 3x²y if (x, y) = (0, 0) + y? if (x, y) = (0, 0) f(x, y) = { x +

A: In this question, we have to check the continuity of a function of two variables.

Q: Find fx (x,y) and fy(x,y). Then, find fx(-1,-4) and fy (-3,2). 32 f(x,y) = 4x³y² fx(x,y) =

A: We have to find partial derivatives of Given function.

Q: 5.) y = x3 + 1, y = 0, x = 1 around the a axis.

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Q: Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

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Q: Find fxy(x,y) if ​f(x,y)=(x^3+y^4)^7. fxy (x,y) =

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Q: . Solve V²u = 0, a <r < b, 0 < 0 < 27, u, (a, 0) = f (0), u, (b, 0) = g (0), 0<0< 2m, where | f ds+…

A: As per the question we have to use the given boundary conditions to deduce the exact solution to the…

Q: Verify that 0t ду дх дх ду 2. 3 y 3 f (x, у) %3D 2х*у — х"у — ху

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Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: Revenue function is given R(x,y) = 19+162x+210y-3x2-5y2-6xy  , it is function of two variable…

Q: = The real part for the function f (z) = 4z2 – 2z + 9 إجابتك = The imaginary part for the function f…

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Q: Decide whether it is possible to solve the equations xu? + yzv + x²z .xyv³ + 2zu -- u?v² = 2 for (u,…

A: 3.7 Given equations are xu2+yzv+x2z=3xyv3+2zu-u2v2=2 The points are  (x, y, z)≈(1, 1, 1) and  (u,…

Q: maximise I1 + 2r2 I3 subject to z + 4r2 + 13 0, I2 unrestricted

A: The given problem is maximize x1+2x2-x3 subject to x1+4x2+x3≤1,-2x1+x3≤x2,4x1+2x3≥-7,x1≤0,x3≥0,…

Q: f(x, y) = x4 + yA; x2 + y2 = 18

A: In this question, we find the maximum and minimum value of the function by using the Lagrange…

Q: Find the linear approximation to the equation f(x, y) xy at the point (4,8,4), and use it to…

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

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Q: Find div(F x G) = V. (F x G). F(x, y, z)= i + 7xj + 8yk G(x, y, z) = xi - yj + zk

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Q: Describe the domain of : Зху 3) f(x, y, z) = 4) f(x, y, z) = 1- x² – y2 – z2 %3D z - Vx

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