p(z) =x2 (n-1) (z + 1 What is the degree of this polynomial function p(x)?
Let P(z) be a polynomial of degree n 2 1. Then CA. P(z) is analytic and bounded on C B. P(z) is not analytic but bounded on C C. P(z) is analytic and unbounded on C D. P(2) is bot analytic and unbounded on C
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r). 1. Consider the polynonial Pl (z) of degree 4...
(c) Iff is a polynomial function of degree n, then f has, at most, n-1 turning points. First, identify the degree of f(x). To do so, expand the polynomial to write it in the form f(x) = a,x"+an-1*"-1 + ... + a,x+20- f(x) = + (2x2 + 7)? (x2+6)
11. Prove that ifp is a polynomial of degree n , and ifp(a)-0, then p(z) = (z-a)q(z), where q is a polynomial of degree
Problem 10.13. Recal that a polynomial p over R is an expression of the form p(x) an"+an--+..+ar +ao where each aj E R and n E N. The largest integer j such that a/ 0 is the degree of p. We define the degree of the constant polynomial p0 to be -. (A polynomial over R defines a function p : R R.) (a) Define a relation on the set of polynomials by p if and only if p(0) (0)...
Please answer problem 4, thank you. 2. The polynomial p of degree n that interpolates a given function f at n+1 prescribed nodes is uniquely defined. Hence, there is a mapping f -> p. Denote this mapping by L and show that rl Show that L is linear; that is, 3. Prove that the algorithm for computing the coefficients ci in the Newton form of the interpolating polynomial involves n long operations (multiplications and divisions 4. Refer to Problem 2,...
The polynomial of degree 4 The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = – 2. It goes through the point (5, 7). Find a formula for P(x). P(x) =
ZEROS OF POLYNOMIAL FUNCTIONS 1. Find a polynomial function f(x) of degree 3 that has the indicated zeros and satisfies the given condition Zeros: -5, 2, 4 Condition: f(3) = -24 f(x) = 2. Find a polynomial function f(x) of degree 3 that has the indicated zeros and satisfies the given condition. Zeros: -1, 2, 3 Condition: f(-2) = 80 f(x) = 3. Find a polynomial function f(x) of degree 3 that has the indicated zeros and satisfies the given...
Problem 2 Let f(x) = sin 2x and P() be the interpolation polynomial off with degree n at 20,***, Im Show that \,f(z) – P() Sin+1 – 20) (1 - 11). (I – In).
Find a polynomial function P of the lowest possible degree, having real coefficients, a leading coefficient of 1, and with the given zeros. 2 + 3i. - 1 and 2 The polynomial of lowest degree is P(x) =