How do I solve this?

4. Show that for some (3 with 0

4. Show that 1 0 for some c with O < c < 1. 1 -f- 51', 30 1 + :r60 c 31' 5. Use the strong Taylor approximation to to degree 3 and the fact that 1 2 for O 0.1 to obtain a bound on the remainder at = 0.1. Use your bound on the remainder to prove a better bound on the remainder by replacing ex 2 by .Y011r improved estimate.