Construct the divided differences table that led to the Hermite polynomial p(x) = 2 – (z – 1) + (z – 1)² +(z – 1)°(z – 3).
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Q: P(x1, x2) = x1X2, Q(x1,x2) = –2x102; D = {(x1,x2) :1 < x1 < 2,0 < x2 < 3}. %3D
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Q: (x? — 2х — 3) у" +ху'+4у %3D 0; хо — 4, Хо 3 — 4, хо — 0 Хо — 4, хо — - 4, хо — 0 |
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Q: Using the equation 2.21 from the textbook (see below) show that TT 1 R t RT -R t T %3D
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- Let P3(x) be the interpolating Lagrange polynomial of degree 3 passing through the points (0,0),(1/2, y), (1,3) and (2,2). If the coefficient of x3 in P3(x) is 6, then determine the value of y.Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2I am trying to find out if the polynomial 12x^4+8x^3+9x^2+4x+4 is reducible or irreducible over Q. We can't apply Eisenstein's criterion here. But we can try this:12x^4+8x^3+9x^2+4x+4 = x^4+(2/3)x^3+(3/4)x^2+(1/3)x+(1/3) x^4+(2/3)x^3+(3/4)x^2+(1/3)x+(1/3)=(x^2+ax+b)(x^2+cx+d) = x^4+(a+c)x^3+(b+d+ac)x^2+(ad+dc)x+bd We get the equation system: a+c=(2/3)b+d+ac=(3/4)ab+bc=(1/3)bd=(1/3) I get the following result:b=(1/2)d=(2/3)c=(2+sqrt(19))/6 and (2-sqrt(19))/6a=(2/3)-((2+sqrt(19))/6) and (2/3)-((2-sqrt(19))/6) The expression in a contains an irrational number, sqrt(19), this means that the polynomial is irreversible over Q. Is this correct?
- H 5. Write down all normalized polynomials of degree at most 4 in Z_2[x]. Underline the reducible polynomials1) consider the degree 4 LFSR given by polynomial p(x)=x^4+x^2+1. What kind of polynomial is this p(x)=?Compute the least squares quadratic polynomial p2(x) which gives the best fit toex over the interval [0, 1]. How does p2(x) compare for accuracy with the Taylor polynomialabout x = 0?
- Find the interpolating polynomial of the following point and function using the Lagrange interpolation process. y = cos ( 2x ) at x = [0,π] with four equally spaced points.Find the second-degree Taylor polynomial T2(x) for the function f(x)=15+x2 at the number x=1.there is at most one polynomial of degree less than or equal to n_____ option,(a) which interpolated f(x) at (n+1) distinct points x0,X1,....xn (b) which interpolated f(x) at (n-1) distinct points x0,X1,.....xn-1 (c) which interpolated f( x) at n distinct points x0, X1,.....xn-2 (d) which interpolated f(x) at (n-1) distinct points x0, X1,. xn-3