5.

(a) Prove that for all x E [0,1]'

x2 x3 9 x2 x3 1 + x + - + - < eX < - + x + - + -. 2 6 - -8 2 6

(b) Prove that for all x E [0,1]'

x3 1 x3 X - -3 -< arctan x -< -4 + x - -3 .

(c) Prove that for all x E [1,2] and y = x-I, y2 y3 y4 y2 y3 y4 Y - 2 + 3 - 4 :::; log x :::; y - 2 + 3 - 64·