Chapter 10, Problem 55RE

find the nth Maclaurin polynomial for the function

Find the standard factorization of the entire function f(z) = cosyz

Find the function’s Taylor polynomials of degrees 1, 2, and 3 centered at c = 0.

Let f(x) be a function tabulated over 4 points, as shown in the table below. Using a degree 3 Newton interpolating polynomial, obtain an approximation for f(2.22). Fill in the table below with the values ​​of the Split Differences up to order 3, as seen in the video lessons. Then enter the value obtained as an approximation of f(2.22) using the Newton polynomial of degree 3. Perform the calculations with 4 decimal places and rounding. Use comma as separator for fractional values ​​(Ex: 3.145 instead of 3.145).

Determine an approximate value of f(8.83) utilizing Lagrange interpolating polynomial of degree three if f(8.75) = -294.25, f(8.80) = -372.20, f(8.85) = -502.15 and f(8.90) = -762.10.

Let y=f(x) be a cubic polynomial with leading coefficient, a=1; containing the ordered pair (2,0) and a zero at x=2i. Find the function, f(x), that has these characteristics.