Find the local linearization of f(z) =z² at 9. lo(z) = %3D

Q: Find the gradient of the function at the given point.

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Q: Find the linearization of f(x) = xm around r = e. Round the gradient and y-intercept, whenever…

A: First we have to find derivative of the given function.

Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

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

A:

Q: Find the partial derivative. f(p, q) = ev af

A: From the given problem; fp,q=e6pq As we know that: The chain rule: fgx'=f'gx·g'x The Power rule:…

Q: Find the orthogonal trajectories of the family of curve y = 3x+c,where c is an arbitrary constant.

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Q: Find the orthogonal trajectories of the family of curves xy = a where a ≠ 0is an arbitrary constant.

A: Consider the equation: xy=Cy=Cxy'=-Cx2 Substitute the value of C in the first derivative:…

Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

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 direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

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Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Find the linearization of y=√x  at a=49. Then use your linearization to approximate √56. Show work

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Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Find the partial elasticities of z = x'e.

A: Introduction: The partial elasticity of z with respect to x is given by, εx=zxxz The partial…

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: In x Find the linearization of f(x) = xmª around x = e. Round the gradient and y-intercept, whenever…

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Q: (6) Find the orthogonal trajectories of the family of curves y = ax? + 4ax + 4a, where a being…

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Q: Find the maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

A:

Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

Q: Find the orthogonal trajectories of the given family of curves. y = (1+C1 x)/(1-C1 x)

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Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: y6 = C (x² + 1) %3D

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Q: Determine the Linearity of this DE. * y" -xy' + y =D0 O Linear O Non-Linear

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Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: Find the gradient function for: 1+3x 1) y = %3D x2 +1

A: Given that  y=(1+3x)/(x^2+1) To find the gradient of y

Q: Find the direction at which the function f(x, y, z) = x In(e – xz) increases fastest at (-2, 0, 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

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

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Q: Find the partial derivative. 3p f (p, q) = e af

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Q: Find the linearization of the function at the given point. f (x, y) = e sin y, 0, 7).

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

Q: Find the orthogonal trajectories of y = e where a be the arbitrary constant.

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Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 5z) at the point (- 1, 1, 2).

A: We have to find

Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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Q: ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter

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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 orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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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) =

A:

Q: Find the linearization of the function f (x, y, z) = -6xy+ 9yz + 8zx at the point (1, 1, 1)

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

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

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

A: Given,  ey+2x2=k

Q: . Find the linearization of √ x at a = 49. Then use your linearization to approximate √ 56.

A: I am going to solve the given problem by using some simple calculus  get the required result.