The data in Exercise 10 were taken from the following functions. Compute the actual errors in Exercise 10 and find error bounds using the error formulas and Maple. a. fix) = tan 2x b. fix) = e~x I -|- x

1 MATH 205 LINEAR ALGEBRA SUPPLEMENT STEVEN H. WEINTRAUB 1. Coordinates and Change of Basis Deﬁnition 1.1. Let B = {v ,v1,..2,v } bn a basis for the vector space V . Let v ∈ V so that v = c 1 1 c 2 +2▯▯▯ + c vn n for unique scalars 1 ,2 ,...,n . The scalars 1 2c ,...nc are called the coordinates of v in the basis B, and the vector c1 c2 [v]B= . . c