# 数学Assignment代写 MATH 142B Assignment 1B

## MATH 142B Assignment 1BDue: 11:59 pm pacific time on Friday, April 9

### Only complete this assignment if you have been assigned to Group B.If you have been assigned to Group A, complete Assignment 1A instead.  数学Assignment代写

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• Late assignments will not be accepted.

### Only complete this assignment if you have been assigned to Group B.If you have been assigned to Group A, complete Assignment 1A instead.  数学Assignment代写

1. Abbott Exercise 2.4.9.

2. Fully justify your answers to the following problems.
(a) Abbott Exercise 2.7.2(a).
(b) Abbott Exercise 2.7.2(c).
(c) Abbott Exercise 2.7.2(e).

3. (a) Abbott Exercise 2.7.4(a).
(b) Abbott Exercise 2.7.4(b).

4. Consider the sequence {xn} where

Determine lim sup xn and lim inf xn. Fully justify your answers.
5. Suppose {xn} is a bounded sequence and {xni} is a subsequence. Prove that

Remark. It can similarly be proven that

1. Suppose {xn} and {yn} are bounded sequences with xn ≥ 0 and yn ≥ 0 for every n ∈ N. Prove that

lim sup(xnyn) ≤ (lim sup xn) (lim sup yn).