Let xj = xo + hj for j = 0, 1, 2. Use the quadratic polynomial interpolating f at those nodes to estimate f' (xo).

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = tan x, a = π

A: The linearization of a function f(x) at x = a is, Now differentiating  given function with respect…

Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: Let f(x, y, z) = 5x³ – y + z?. Find the maximum value M for the directional derivative at the point…

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Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

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: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: Let fn(x) = E s;(x) Y; be a linear smoother. Find a condition on the weights s;(x) so that fn(x) is…

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Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

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: Find the maximal value of the directional derivative of w = xy°z at the point (2, 1, 1)

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Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: xy ,show that: x- y If z = = 0

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Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

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 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: Find the linear approximation of f(x) = In r at a = 1 and use it to estimate In(1.14). L(2) = %3D…

A: Please refer the attached image for complete solution.

Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

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Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: Let f(x, y) = x² + In(2x – y). Find the gradient Vf(x, y) at the point (1, 1). O O O O

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Q: Verify by differentiation that a) / t dt : V1+t2 /1+t² + C; _ b) tan(x)dr = – In(cos(x)) +C, –1/2 <…

A: Given to find ∫t1+t2dtPut 1+t2=udifferentiate 2tdt=dutdt=du2therefore…

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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

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Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

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Q: Find the linearization L(x) of f(x) = cot x at x = 4 %3D -

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Q: Find the gradient field for the function f(x, y) = x2+y2

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Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

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Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Solution: Consider the given linear transformation : Dxf = 2x + 3 Since D is the linear…

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 lineanzation LlXiy) of f (iy) =x*-5Xy at (2,1). Then use the linearization to approximate f…

A: Here in this question we need to linearize the given function and then approximate the value of…

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

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

A: Explanation: The Linear Approximation should be a line that can substitute (in a narrow interval)…

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

A: Given: y=mx+b

Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

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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 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 that F = 12x²yi + (4x + 8yz²)j + 8y² zk is conservative, and find a function f such that F =…

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Q: Show that the functions ƒ 1 (x) = sin x, ƒ 2(x) : = cos x, and f 3(x)=x cos x are linearly…

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.