Show that the Newton divided-difference polynomials 3 - 2(х + 1) +0(х + 1)х + (х + 1)x(х — 1) and -1+4(х+ 2) - 3(х + 2)(х + 1) + (x+2)(х+ 1)х keth interpolate the data (-2, –1), (–1,3), (0, 1), (1, –1), (2, 3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?

Q: Show that the Newton divided-difference polynomials 3 - 2(х + 1) + 0(х + 1)x + (х+ 1)x(х — 1) аnd…

A: Given,

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: The first four Hermite polynomials are 1, 2t, -2+ 4t²,and -12t + 8t3. These polynomials arise…

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Q: Use Gauss-Jordan method to calculate the inverse of A A-l = |1 0 -1 A =| 0 1 1 1 1 1

A: By Gauss Jordan Elimination method the inverse of matrix is given as follows :

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Q: a) Calculate f(3.4) using Newton's interpolating polynomials of order 1, 2 and 3. All numeric values…

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Q: •Use the Newton backward-difference fomula to construct interpolating polynomials of degree one,…

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Q: Consider the data (1,10), (3,6)(1,10), (3,6). Then, Newton's polynomial that interpolates the data…

A: Solution of given problem is followed by Newton's interpolation formula.

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Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

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Q: Show that the Newton divided-difference polynomials 3 — 2(х + 1) + 0(х + 1)х + (x + 1)x(х — 1) and…

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Q: Determine the third and fourth Taylor polynomials of cos xat x = π.

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Q: 6. Show that when ) < |z - 1| < 2, e - ( - 3) (2 - 1)(2 – 3) Complex Analysis n=0 (z-1)" 2+2 2(z-1)

A: We use Laurent series to prove given example.

Q: Use Lagrange interpolating polynomials of order 4 to calculate (7.1) 1 3 8 Ax) 1 20 94 267

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Q: Find the string that has this generating function: a) (1− x)−3 b) (1+2x)−4 c) 1/(1 −3x)3

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Q: Test the sets of polynomials for linear inde­pendence. For those that are linearly dependent,…

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Q: Determine the third degree Newton polynomial which passes through the data points (0,1); (1, 0); (2,…

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Q: 2- Use the Newton backward-difference formula to construct interpolating polynomials of degree one,…

A: formula for newton backward difference is  y r = y+ r∆y+ rr+12!∆2y _...   where r =x-xnh

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Q: Let f(x) = x - x. Construct the divided-difference table based on the nodes xo = 1, x1 = 2, x2 = 3,…

A: Let , fx=x3-x And , x0=1 , x1=2 , x2=3 , x3=4 , x4=5 , x5=6 Then , calculate fx x 1 2 3 4 5 6…

Q: b) Show that P1(cos(0)) and P2(cos(0)) are orthogonal to each other, P, and P2 being Legendre…

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Q: Calculate the first three Legendre coefficients for f (x) = x² + 1 and then express the f(x) in…

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Q: 1. The specific heat capacity Cp[J/mol/°C] is often correlated to temperature T[°C] in form of a…

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Q: Test the sets of polynomials for linear inde­pendence. For those that are linearly dependent,…

A: We have to determine whether or not we can find real numbers r, s,t, which are not all zero, Such…

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: x3 + (2i – 1)x³ – 2ix – 5 a = 1- i -

A: Given: The given polynomial is x5+2i-1x3-2xi-5 a=1-i into binomial.

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have to use the Euler method

Q: 2. Consider the data: X 0.1 0.2 0.3 0.4 0.5 f(x) | 1.40 1.56 1.76 2.00 2.28 Use the Newton's forward…

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Q: Show that the Newton divided-difference polynomials 3 – 2(x + 1) + 0(x + 1)x + (x + 1)x(x – 1) and…

A: Given: Let P(x)=3-2x+1+0x+1x+x+1xx-1    Q(x)=-1+4x+2-3x+2x+1+x+2x+1x

Q: 4. a) Let P3(x) (classical) be the interpolating polynomial for the data given in Table 1. Find y if…

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Q: Calculate f (3.4) using Newton.s interpolating polynomials of order 1 through 3 and estimate the…

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Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of 1- 1?

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Q: 1- The Newton's divided interpolating polynomial on x, = x,-1 + 0.25, Vi=1,2,3 , xo = 0 given by…

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Q: Example 7.4. Using Newton's backward difference formula, construct an interpolating polynomial of…

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Q: 1. Construct interpolating polynomials P1(x), P2(x), and P3(x) of degrees 1, 2, and 3 respectively…

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Q: -2 21 -9-21 1- FIND THE INTER POLATION POLYNOMIAL BY USING THE FOR THE ABOVE NEWTON DIVIDED…

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Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x?,1 + x + 4x²,1 – 7x

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Q: Q2) Determine whether the given polynomials form an orthonormal set, and if not, use Gram-Schmidt…

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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: 8. In Newton-cotes formula, if f(x) is interpolated at equally spaced nodes by a polynomial of…

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Q: polynomials

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Q: 1- Using Newton's backward difference formula, construct an interpolating polynomial of degree 3 for…

A: When the value of function at certain equally spaced points is known then the Newton's backward…