:Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find interpolates f (0.25) also estimate the error. X 0.2 0.22 0.24 0.26 0,28 0.29 Sin x 0.1987 0.2182 0.2377 0.2571 0.2764 0.2860

Q: Given a function ƒ (x). Suppose that, the Newton's interpolating polynomial P2(x) of f (x) at the…

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Q: B/ Given a polynomial function with following data points: Find x f(x) 0 3.6 1.5 1.8 3 1.2 4.5 0.9 6…

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Q: (d) Let G be the function given by G(x) = f(t)dt. Write the third-degree Taylor polynomial for G…

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Q: Compute the Taylor polynomial T3(x) and use the Error Bound to find the maximum possible size of the…

A: Given f(x)=cos(x), a=0, x=0.175

Q: (a) Find the equation of the following curve Ax) using Newton's divided difference polynomial.…

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Q: b) Let f(x) = e"cos 3x, No 0, x = 0.3,1 =0.6, n = 2 %3D Construct the second Lagrange polynomial for…

A: We have fx=e2xcos3x Now,  x0=0x1=0.3x2=0.6 Therefore,  fx0=e20cos30=1fx1=e20.3cos30.3=…

Q: tion 10 Jsing Newton's backward difference polynomial of degree 2, for the below data, approximation…

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Q: 5. Let Tn be the nth Maclaurin polynomial for f(x) = e². Find a value of n suc. le01 – T,(0.1)| <…

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Q: Let F(x) = e -5¢4 dt. Find the MacLaurin polynomial of degree 5 for F(x). Use this polynomial to…

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Q: Consider the function x >0 f(x) = |-V-x x 0. Compute r1, x2, X3, X4 . b) Based on (a), what is x,…

A: Given function: →f(x) = x           x≥0--x     x&lt;0

Q: 2. Let g(x) = ev cos +, Approximate the value of g(0.2) using the second degree Maclaurin polynomial…

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Q: 3. The polynomial f(x) = 0.0074x* - 0.284x + 3.355x - 12.183x +5 has a real root between 15 and 20.…

A: Let,  f(x)=0.0074x4-0.284x3+3.355x2-12.183x+5 Hence, f′(x)=0.0296x3-0.852x2+6.71x-12.183   The…

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

A: The given data is f(0)=2 ,f(1)=3, f(2)=12, f(3)=41.

Q: Use the Taylor polynomial of degree four for the function f(x) = e - 5x at x = 0 25 125 625 P4(x) =…

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Q: Q.No.7 From the following table, obtain f(x) as a polynomial in powers of (x-5) using Newton's…

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Q: Compute the Taylor polynomial T5(x) and use the Error Bound to find the maximum possible size of the…

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…By…

Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = 11 tan-1(x), a…

A: The function is givne by,

Q: (a) Given the function f(x) = cos(4x) compute the first, the second and the third derivative: f'(x),…

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Q: Q2: Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find…

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Q: Based on the given function below x0 = 0.15, x1 = 0.25, x2 = 0.30 and x3 = 0.45 Using the…

A: As we can see points are not equidistance so we will use the divided difference method. Formula for…

Q: compute the Taylor polynomial indicated and use the error bound to find the maximum possible sizeof…

A: The given function is

Q: Screen Shot 2021-... >> Consider the function f(x) = Vx + 4. O - Screen Shot 20 Approximate f by a…

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Q: Q) Use the Lagrange interpolating polynomial of degree two to approximate f (0.43) if f (0)=1 f…

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Q: 0.125 0.250 0.375 0.500 0.625 0.750 f(x) 0.79168 0.77334 0.74371 0.70413 0.65632 0.60228 1- Using…

A: Lagranges interpolation formula of order 3  with 6 points (x0,y0),(x1,y1),(x2,y2),(x3,y3),(x4,y4)and…

Q: Use the Linear Approximation to estimate Af for f(x) = - when a = 2 and Ax = -. 5+x2 (Use decimal…

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Q: Consider the function f(x) = We approximate f(x) by the Lagrange interpolating 2a+1 polynomial P,…

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Q: Let P(x) = 3x - 2x³ be the Lagrange interpolating polynomial that approximates a function ƒ over the…

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Q: Use Newton's Method to estimate a root of the function f(x) = x + 2 - e Use the initial estimate 1 -…

A: We need to find x7.

Q: 5) Find the velocity of rocket by using Gregory-Newton interpolation polynomial at t=260 sec. time…

A: Consider the given table. We have to find the velocityt=260 sec Since, t=260 sec is near to the…

Q: Q5) Consider the Table below. y, = f(x,) 0.5 25.5 1 1.2 8.75 2.5 12.5 3 3.2 5.25 Find cubic Newton…

A: Given,

Q: Approximate f(1895) using an interpolating polynomial of degree 4 using Newton's forward-difference…

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Q: a) Develop a table of f(x)= e¯* + 5x for x = 2, 4, 5 and 8. b) Estimate f(3.2) using the…

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Q: Let P(x) = 20x* - 7x³ be the Lagrange interpolating polynomial that approximates a function f over…

A: Sol: Px=20x4-7x3Since it approximate the function -1,1Approximation of ∫-11fxdx mus t be equal to…

Q: a) Use the Lagrange estimate of the residual term to find the degree of the Maclaurin polynomial…

A: The Maclaurin series is used to approximate the value of the difficult terms. The series value is…

Q: (a) Given the function f (x) = In(1 – x). compute the derivatives f'(x), f"(x), f'''(x). (b)…

A: Answer and explanation is given below...

Q: Q3. Let f(x) = x + 2 In(x + 1). (а)( (b) (c) ( | Hint: Use only 5-decimal digits in all your…

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Q: Q3: Construct a 3rd order Lagrange polynomial of the function f(x) = lnx.cosx where x e [1, 4]. Then…

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Q: Assume that g(x)=1/x, 0.4≤x≤1.6. Assume that you approximate g(x) by the 2nd degree Taylor…

A: Consider the given function:

Q: Using equally spaced nodes on the interval (0, 0.3. the upper bound for the error of the cubic…

A: Given the interval, a,b=0,0.3                                 fx=sin3x For cubic Lagrange…

Q: Consider the function f(x) = Vx+1. (a) ( Compute f'(x) and f"(x). • (b) the point a = 0. O Write…

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Q: Let F(x) = e -514 dt. Find the MacLaurin polynomial of degree 5 for F(x). - 0.12 -5x* dx. e Sx4 Use…

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Q: a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x² e-2t sinh t…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 17) Find P₁0 (x), the Taylor polynomial f(x)= tan¹ (x³) at a=0. P(x) = x²³ - ²¹ +² the function

A: To find the Taylor's polynomial

Q: A scientist has executed one experiment to identify the values of an unknown function f(x). The…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Compute the Taylor polynomial T3(x) and use the Error Bound to find the maximum possible size of the…

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Q: Use the Newton Raphson Method to find the root of f(x) using 2.2 as the starting value of x. Iterate…

A: f(x) = tan-1x2+x-6 then f'(x) = 2x+11+x2+x-62

Q: Compute the Taylor polynomial T;(r) and use the Error Bound to find the maximum possible size of the…

A: Given: fx=cosx a=0 x=0.175 To find: T50.175, using Tylor's polynomial. Bound for f0.175-T50.175,…

Q: Let Pn be the nth Taylor Polynomial of the function f(x) centered at x = 0. Assume that f is a…

A: Since f(x) is centered at x = 0, we get the error function as M(x-a)n+1(n+1)!

Q: Part a: Find the 7th degree Taylor polynomial for f(x) = x³ e2x centered at x = 0. Part b: Use your…

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Q: A. Compute the bound B of the error when approximating f(x)=sin(x) with a polynomial of degree 1 in…

A: The given function is fx=sin x. Find the error bound for f approximating with a polynomial of degree…