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.

Long division setup showing an incomplete calculation. 12 is in the divisor, 6839 is in the dividend, and 5 hundreds and 6 tens is written in the quotient. 6000 is subtracted from 6839 to give 839. an unknown value represented by a box is being subtracted from 839. what number should be placed in the box to complete the division calculation?