1. Let f(x)=e' and x = [-1, 2]. a. Find an upper bound for the error in the MacLaurin polynomial of degree five. b. If we want the error to be smaller than 0.0001, what degree MacLaurin polynomial is needed? c. If we use a MacLaurin polynomial of degree 5 and we want the error to be less than 0.0001, what interval restriction would we need to have for x?

a. Find the second Taylor's polynomial P,(x) of the function f(x) = cos z about the point to approximate cos 42° (use 4 digit rounding) (3 marks) 6 b. For a function f(x) the forward differences are given by 2o = 4 f[ro] = 52 f(ro, 21] = 9 21 = 5 flæ1] =? f(ro, 21, x2] = 1.5 f[x1, x2] =? 12 = 6 f[x2] =? Find the missing entries in the table. (3 marks)

3.please help

2. Find y at x = 0.3, using 2-degree Newton Polynomial. Show table of divided differences using 3 points x = 0, 0.2, 0.4. Show polynomial used.