Find the linearization L(x,y) of the function at each point. f(xy) =x° + y° + 1 а. (4,4) b. (2,4)

Q: 7x – 4xy = C

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Q: Find the local maximum and minimum values and saddle point(s) of the function f(r, y) = -x4 + 4xy –…

A: Given ,fx,y=-x4+4xy-2y2+1fx=-4x3+4yfy=4x-4yNow,-4x3+4y=0⇒-x3+y=0…

Q: 13. Find an equation of the curve that passes through the point (1, 1) and whose slope at any point…

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Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (B) 2y³ + 2x²…

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Q: Find the linearization L(x,y) of the function at each point. f(x у) — х2 + у2 +1 а. (1,1) b. (4,2)…

A: Solve the given function

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (F) 2y³ + x³…

A: Introduction: An orthogonal trajectory of the family is any curve that cuts each member of a…

Q: Find the gradient of the function at the given point. In(x2 - y) - 2, (2, 3) Z = Vz(2, 3) =

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Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: Which of the following is the orthogonal trajectories of the family of cissoids y² = ? a- y² = C(x +…

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Q: Find the linear approximation to the equation f(, y) = 3. xy at the point (6, 4, 6), and use it to…

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Q: 8 Find the linearization L(x, y) of the function at the given point f(x, y)=1+xIn(xy-5), (2,3)

A: Given: f(x,y)=1+xln(xy−5)(2,3)L(x,y)=?

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (2,4)…

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Q: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

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Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: Find the gradient of the function w = 2x?y- 4yz + z² at the point (1, 1, -2). O 2î+ 18ĵ- 6k 4î+ 10j-…

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Q: 6 Determine the position and nature of the stationary points of the functions: (a) z= 2x²y² + 4xy² –…

A: stationary points are those points of function f(X) where its gradient is ∇f(X) = 0 if hessian…

Q: Find the orthogonal trajectories of the family of curves x²- y2=C² A) x- y=C (B xy3=C xy=C D…

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Q: 6. State whether the equation is ordinary or partial, linear or nonlinear, and give its order. (x +…

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Q: Find the orthogonal trajectories of a - =1; where 2 is an arbitrary parameter. a + 2

A: This is a question of the Differential equation.

Q: (6) Find the orthogonal trajectories for the given families of curves 2x2 – 7y = c.

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Q: y6 = C (x² + 1) %3D

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3)

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Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: b. Find the partial derivatives fx ,fy of the f (x,y) = x². e²y+3x

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Q: Q.NO.2: a) Find the equation of the orthogonal trajectories of the family of curves. x²y² = 4c²

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: w = 3x² – 5y² + 2z², (1,1, –2)

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Q: Find the orthogonal trajectories of the family of curves y = ce^x. Select the correct response: x^2…

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Q: 2. A curve is such that = 2(3x + 4)3/2 – 6x – 8. Given that the stationary point on the curve has…

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Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

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Q: If the function f(x, y) = ;x³ + y² + 2xy – 6x – 3y + 4 has one saddle point (a, b), then 46 + a = -

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Q: (b) Classify the equation t - 2ty +2y =t, t> 0. What order is it? Is it linear or nonlinear? Is it…

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: : @ use suitable linearization to find the approximate value for the Function at point p. f (xy) =…

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Q: Q3:Find all the second order partial derivatives of the f(x,y) 2x* - 5x'y3-y3

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Q: Find the partial derivatives of the function V1r2 + 1s² + 6r² w =

A: Given,  w=1r2+1s2+6t2

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: Find the directions of maximum and minimum change of f at the given point, and the values of the…

A: Given :   f(x,y) = 4y2e3x  Point : ( 5,2)

Q: onsider the DE vy" – y' + y = 0. ) Is this DE linear? ) If it is linear, is it omogeneous?

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Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: Determine whether the functions y1 and y2 are linearly dependent on the interval (0,1)

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Q: Find the partial derivative with respect to z of the function (3a – 2)e2y-5 In(-5z - 1).

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Q: Q3:Find all the second order partial derivatives of the f(x,y) = 2x*- 5x'y-y3

A: the given function is  f(x, y) = 2x4 - 5x3y3 - y3

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: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Find the linearization L(x, y, z) of the function f(x, y, z) = V2x² + 3y² + 3z? at the point (2, 2,…

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