Obtain the Legendre polynomial Ps(z) by application of the recurrence formula nPn(x) = (2n-1)xPn-1(2)(n-1)Pn-2(x) assuming that P₁(x) and Ps(r) are known.

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

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Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Using P3(x) =[5x³ – 3x] and P4(x) =[35x* – 30x? +3], generate the next Legendre polynomial using…

A: It is known that the Legendre polynomial satisfies the following recurrence relation.…

Q: ve that if x5 – 3x4 + 2x

A: Introduction: In an equation, the two expressions are assumed to be equal, as indicated by the…

Q: If the sum of the coefficients of all even powers of x in the product (1 + x + x² + ... + x2n) (1 –…

A: Introduction :

Q: If we multiply the Legendre polynomial of degree n by an appropriate scalar we can obtain a…

A: Definition:

Q: Find the coefficient of x5 in (1 – 2x)-7 using generating function.

A: Given to find the coefficient of x5 in 1-2x-7 The generating function will be Gx=1-2x-7…

Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

A: Given: ∫abf(x) dx and the function f(x), where the interval of integration a, b is divided into n=3…

Q: Expand the f(x) = 10 + 8x +9x² in a seried of Legendre polynomials. O a 13P,x)– 8P,(x) – 6 P, (x) O…

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Q: Indicate the least integer n for which (3x6 + 2x2)(x3 + 3x) is O(xn).

A: Solution:-

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and…

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Q: 4) For Bernstein polynomial, B₁ (f; x) = Σk=o (k) x* (1 − x)"-kƒ (), we have B₁ (2t² + 1;x) = 2x² +…

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Q: What is the value of f(-2) of the polynomial f(x) =-a + x + 1? What does this mean about the linear…

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Q: In Horner's method suppose x0 is a root of p(x). show that the numbers bk(x0) produced by…

A: a. Let the polynomial be  Px=∑k=0nakxn-k                   (i) Given that x=x0 be a root of the…

Q: 1+ 3k 1- 3k] 1 – 3k 1+3k 2 - prove that AK: 2 1 For A : -1 -

A: Given, A=2-1-12   ...i    ....(i)  We need to show that Ak=121+3k1+3k1+3k1+3k    ...ii     Now, A…

Q: Determine whether or not the given polynomial is irreducible over Q (a) x4 - 10x² + 1 (b) (5/2)x+…

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Q: Prove this Adams-Bashforth method using polynomial interpolation and prove it's second order…

A: As per the question  we have to derive the two-step Adams-Bashforth method by using polynomial…

Q: Find the coefficient of x25 in the generating function (x+ x2+ x3 + x* + x5+ x®) 4 (x²+ x³ + x*+..a…

A: Given function is, x+x2+x3+x4+x5+x64x2+x3+x4+...3 Now, we can write the given equation as,…

Q: Find p(1) and p (-3) of each polynomial. p(x) = x4 - x3 + x - 1

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Q: Find the fifth Taylor polynomial of x3 - 7x2 + 8 at x = 0.

A: Given: fx=x3-7x2+8

Q: It is possible to write rk as a linear combination of Chebyshev's polynomials, for example Suppose…

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Q: Calculate Sxe 0 re-L₂ (x)L(x)dr by using Recurrence relation of Laguerre function, Ln

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Q: Show that, if gcd(a,n)=gcd(a-1,n)=1 then a is a solution of the polynomial parity x² + ... + xó(n)-1…

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Q: Given (xi, x2024) Vi = 0,...,n, where x0 = -1, x₁ = 0, x2 = 1, x3 = 2, ..., xn = n = 1. Write down…

A: (a). When n=1, we have to points: (x0​,x02024​)=(−1,1) and (x1​,x12024​)=(0,0).  The interpolating…