Find the linear approximation to f(x) = at a = 4.

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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

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Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: Using a local linear approximation of f(x) = v4 + x at a 0 to estimate the value of v4.3 gives

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Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

Q: y = x – 2 + Ce* X-

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Q: Find the orthogonal trajectories of Vy= = CX

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Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

Q: verify the given linear approximation at a=0 . Then determine the values of x for which the linear…

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Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function.  F(x) = (1 / x) , a = 2

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

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

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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 linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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Q: Find the gradient of the function z = ln(x2 − y) /(x − 4), at the given point     (2, 3)

A: To find the gradient differentiate z partially with  respect to x and y. Given function  z=lnx2-yx-4…

Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Find the critical point of the function f(x, y) = 8 – 4x + 7x² – 6y – y? - -

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Q: ) Find the local linear approximation of the function f(x) = V1+x at xo = 3, and use it to…

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Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: Find the linear approximation to f(x) = (x+2) at 0 and use it to approximate (2.001)

A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

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Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Find the linearization of the function f (x) = a° at a = 1.

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Q: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

A: y=2x2+7x+4, ∆x=0.3 & x=5 Differentiating with respect to x, we get dydx=22x+71+0=4x+7 Now at…

Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: Find the linearization of the function f(x)=x5 at x=1. L(x)= Using this linearlization, f(1.04).is…

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Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given function is, h(x)=x4.

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 linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Find the linear approximation of f(x)=(1+x)3 at x=0. Using this approximation to estimate (1.01)3…

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

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