Let {(−1,−5),(0,−4),(1,−1)} and {(−1,14),(0,7),(1,4)}
be the point-value representations
of two polynomials f(x) and g(x). Find the point-value
representation of h(x) = f(x) +g(x).
From the point value representation of h(x) find the coefficient
representation of h(x).
Let {(−1,−5),(0,−4),(1,−1)} and {(−1,14),(0,7),(1,4)} be the point-value representations of two polynomials f(x) and g(x...
(1 point) Let f(x) = 0 if x < -4 5 if – 4 < x < 0 -3 if 0 < x < 3 0 if x 2 3 and g(x) = Los f(t)dt Determine the value of each of the following: (a) g(-8) = 0 (b) g(-3) = 5 (c) g(1) = (d) g(4) = (e) The absolute maximum of g(x) occurs when x = 0 and is the value It may be helpful to make a graph...
The f function differentiable at (-1,4) and 7(3) = 5 also let Hx f'(x) > -1. Find the greatest value f(0).
Example 39. Let So, for x € (-1,0); f(x) = | 1, for x € (0,7). and let f(x) be 27 -periodic. Find the Fourier series of f(x). { 9
let f(x) and g(x) be two polynomials with rational coefficients. Let d(x) be the greatest common of f(x) and g(x) in Q[x] (Q as in the set of rational numbers) and e(x) the greatest common divisor of f(x) and g(x) in C[x] (C and in set of complex numbers). is d(x) = e(x)
5. Let V be quadratic polynomials on the interval [-1,1], with the inner product 〈f,g):= | f(t)g(t)dt, and D VVfHf be the differentiation operator. (a) Find the Hermitian transpose (adjoint) D, which is determined by its action on a basis, by calculating D'(1), D*(x), D'(x2), explicitly. Find the eigenvalues and corresponding eigenfunctions of D* (c) Find (D) 5. Let V be quadratic polynomials on the interval [-1,1], with the inner product 〈f,g):= | f(t)g(t)dt, and D VVfHf be the differentiation...
4. Let F be a field. Prove that for all polynonials f(x), g(x), h (z) є FI2], if f(x) divides g(x) and f(z) divides h(r), then for all polynomials s(r),t() E Fr, f() divides s()g(r) +t(x)h(r). 4. Let F be a field. Prove that for all polynonials f(x), g(x), h (z) є FI2], if f(x) divides g(x) and f(z) divides h(r), then for all polynomials s(r),t() E Fr, f() divides s()g(r) +t(x)h(r).
6. Let p;(xi = 0,... , n}, with degp;(x) = i, be a set of orthogonal polynomials with respect to the inner product f f(x)g(x) dx. Given a < b, let q(x) be the line mapping a to -1 and b to 1. Prove {p;(q(x))|i = 0,... , n} is a set of orthogonal polynomials with respect to the inner product f(x)g(x) dz, satisfying deg p;(q(x))= i - 6. Let p;(xi = 0,... , n}, with degp;(x) = i, be...
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of degree 0 and 1, 3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of...
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13 Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
Let f(t) = 2t + 4. f-1(s) Let g(x) 2 + 1 g-(3) Below is an input-output table for the function h(x). х h(x) 2 0 1 1 2 الها 3 1 4 0 h-(3) = Now consider the following graph: 5 3 2 -5 -4 -3 -2 -/ 2 Cat 3 4. -2 3 -4 -5+ q