Find the linearization L(x) of f(x) at x=a f(x)= x+1/x a=3 show all work

Q: 1-Find the gradient of (1) f (x,y)= In(x²+y²) (1,1)

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Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the…

A: Given that, A system of the type x˙=fx, fx=-grad Vx is called a gradient system.  Investigate the…

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: What is the formula for the linearization of a function f at the point x = a? %3D

A: Given :To provide the formula for linearization of a function f at the point x=a

Q: What is the linearization L (x) of a function ƒ(x) at a point x = a? What is required of ƒ at a for…

A: linearization is finding the linear approximation to a function at a given point.It is given by,

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

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

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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: Make an example of an autonomous ODE, with stable equilibrium at -1 and 3, and an unstable…

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Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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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: Use the application of Calculus. TOPIC: Partial Differentiation. Solving Using the Definition az If…

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Q: Let ƒ (x, y) = x³ − x² − 8x + 2xy − - - 12y². (a) Compute all first order and second order partial…

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

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: Find the Linearization L(x) of y= (3+ x)-1/2 at a = 1. L(x) =

A: To find the Linearization.

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: find a linearization at a suitably chosen integer near a at which the given function and its…

A: (1)Given:

Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: 2] write the chain rule formula for the derivatives Of and E , where Z=ZCrisit).

A:

Q: Find the linearization of the function at x = 1. * f (x) = 2x³ - 3x + 7 O y = 6 + 1(x - 3) O y = 6 +…

A: Given, fx=2x3-3x+7

Q: (f) Classify the partial differential equation which represents parabolic or hyperbolic or elliptic:…

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Q: 8. Find the orthogonal trajectories of y = cx CX

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

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

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Q: (b) Find all first and second partial derivatives of z = x² In(x² + xy).

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: 3. Let f(x, y) = In 2x + 4y, find the directional derivative of f(x, y) in the direction of at the…

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Q: Consider the functions f(x, y) = x2 − y2 and g(x, y) = x2 + y2 .                             (a)…

A: Given functions are f(x,y)=x2-y2  and g(x,y)=x2+y2.

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

A: for finding gradient we have to find the derivative with respect to x and y   z  = ln(x2 -y)/x - 3…

Q: Find the linearization L(x.y) of the function f(x.y) = 2x- 7y + 3 at the points (0,0) and (1,1). The…

A: f(x,y)= 2x-7y+3 fx  = 2 fy = -7 The linearization of a function f(x,y) at (a,b) is given by L(x,y) =…

Q: Let f(r,y, z) = x² + 3x°y + z°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: Find the linearization L(x, y) of the function f(x,y)= at the point (1,2) and use it to 3xy…

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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: Verify the chain rule y = t³. %3D

A: Given query is to solve the expression using chain rule of derivative.

Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: x2 - y2 + 2Cx = 0

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Q: 1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example

A: We have to solve

Q: 8. Find the orthogonal trajectories of CX

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Q: Find all the second order partial derivatives of the given func f(x.y) = xy2 + yex + 5 A.

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Q: Find the linearization of the function z =/ at the point (-5, 1). L(1, y)

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Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

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Q: Let f (x, y) = x3 – 3xy + y3. Find all critical points of f and at each critical point, - use the…

A: Critical points using second derivative test

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.