Answer Happy

numerical analysis,
1. a a. Below is a table of values for a function f defined on the interval (0,3). 0 1 2 3 f(x) 3 5 3 1 Construct P3(1), the Lagrange interpolating polynomial of degree 3 to interpolate the data above. b. Suppose the table above was generated using f(x) = 2 sin(4x) + 3. i. Find an upper bound for the absolute error in approximating f(0.5) by P3 (0.5) and compare it to the actual error. ii. Find an upper bound for the absolute error in approximating f(x) by P3(x) on the entire interval (0,3]. iii. Use the software package of your choice to graph f(x) and P3(x) on the same set of axes for 0<x<3