This question is to be completed using Matlab.

(a) (3pts) Determine the error and convergence rate for the forward difference method for the derivative of the function f(1) = sin(x) at 2 = 0 (see example from class). (b) (3pts) The order you will see is different than what the theory gives us. What does the theory say? Is there an error in the proof (why, why not?)? (c) (6pts) Create the Taylor expansion at r = 0 for sin(1) up to n = 6. Can this explain what is happening in a)? (a) (3pts) Determine the error and convergence rate for the forward difference method for the derivative of the function f(1) = sin(x) at 2 = 0 (see example from class). (b) (3pts) The order you will see is different than what the theory gives us. What does the theory say? Is there an error in the proof (why, why not?)? (c) (6pts) Create the Taylor expansion at r = 0 for sin(1) up to n = 6. Can this explain what is happening in a)