Exercise 3.4.10: a) find a continuous f : (0,1) → r and a sequence {xn} in (0,1) that is cauchy, but such that { f(xn)} is not cauchy. b) prove that if f : r → r is continuous, and {xn} is cauchy, then { f(xn)} is cauchy.

Aproduction manager test 10 toothbrushes and finds that their mean lifetime is 450 hours. she then design sales package of this type of toothbrush. it states that the customers can expect the toothbrush to last approximately 460 hours. this is an example of what phase of inferential statistics