(2) Let f(x) = cos (2x). Find the Hermite interpolation H3(x) using xo = 0 and x1 = , and use error formula to find the error bound of /(풍)- Hs(풍).

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian. b. Establish…

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Q: Use Chain Rule to find given w = ds x2 – 2y + z2 and a = cos (st), y = -2s In t and z = s – - VE.

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Q: Let X ~ Poisson(λ). Derive the moment generating function of X and use that to find E(X3)

A: Solution: Let X~Poisson(λ) The probability distribution of X is  P(x)=e-λλxx!    x=0,1,2,3,..

Q: (b) State (without proof) the dimension formula for the linear transforma- tion L:V → W where both…

A: Dimension theorem

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

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Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: Find the in tervals on which f are: (il In creassing and decreasing Con cave uP and con cave down…

A: Here, the given function is: y=sin22x, [0,π]

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Let & be a minimax estimator of 0 under the squared error loss. Show that co+ c1o is a minimax…

A: Given that: δ be a minimax estimator of θ under the squared error loss. sinx+1=0sinx=-1…

Q: Let f(x) = -cos(x). Compute ộ = coto + C1T1 where to = 1 and 1i = x. %3D Compute the discrete…

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Q: Solve the ODE: xy"+2y'-xy Oby using the Frobenius method.

A: Given that ODE: xy''+2y'-xy=0                    .....1 We know that the solution to this ODE is:…

Q: Find the best rank 2 approximation to A from (1) with respect to ||:||F.

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Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: ==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

A: The Stoke's theorem states that ∫CF·dr=∬S∇×F·dS Where z=gx,y and dS=-gx,-gy,1dxdy.

Q: Using the Method of Undetermined Coefficients, a suitabie choice for the nonhomogeneous solution yw…

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Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: 1. Find the maximum of the function: f (x) = 4sinx (1+ cosx ) a. Using Golden Section Search with…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: 1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

A: Solve the following

Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: Evaluate the integral. x² - 81 | V=² x x² - 81 | Vx² x √x². 81 X √x². 81 X x² - 81 X 1² 1² - dx = -…

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Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

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

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Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

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Q: Suppose that w = x² + y² – z² | And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: Simplify w by substituting values of x , y and z and then solve the partial derivative.

Q: Show that e, sin x, cos x are linearly independent using Wronskian Method.

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Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 3n/2 %3D

A: We have to find the linearization L(x) of the given function.

Q: 2. Use partial differentiation to approximate the following sum, not the individual radical. V81 +…

A: According to question,Given expression,81 + 263

Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: Show that the family of functions {s()}" COS n=0 is mutually orthogonal on -L≤ x ≤ L, with respect…

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Q: 2. If the Wronskian of y1 and y2 is e2" (x² + 5) and y1 = e2", find y2. %3D

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Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

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Q: 8. Use the Chain Rule to find az/as and az/at. z = (y-2x)³, x = s³t², y=s+t²

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Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du as…

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Q: (c) Apply the golden ratio search method to locate the minimum of the function f(x) = 4x³ – 20x +…

A: Solution:

Q: 1. Find the optium path for f=xy³ from (2,1,2)

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Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: Find the Wronskian for y, = sin 3x , and y2 = cos 3x.

A: The Wronskian, W, of two functions, f and g is calculated as follows. W=fgf'g' , where, f' , g'are…

Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: 2) Find the 3 Taylor pelynomial P,(x) of fix) = Sinx at X = * ½

A: