Use the following steps to prove that the sequence xn has no convergent subsequences if and only if ix n i + 00 as n + 00. a) suppose that the sequence xn has no convergent subsequences. let m > o. prove that there exist at most finitely many values of n such that xn e [-m, m]. explain why this implies ixn i + 00 as n + 00. b) suppose ixn i + 00 as n + 00. show that xn has no convergent subsequence. (hint: exercise 1.61 may .)

Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.