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Answers to homework set #2 CC-BY-NC

Maintainer: admin

Student-provided answers to homework set #2, due date unspecified (not to be handed in and thus not marked). The content on this page is solely intended to function as a study aid for students and should constitute fair dealing under Canadian copyright law.

Problems to complete: all problems in (4.1), (4.2), (4.3) (but 4.3 is not emphasized).

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1Section 4.1

1.1Question 1

Determine a condition on |x1| that will ensure that
(a) |x21|<1/2

|x21|=|x1||x+1|. If |x1|<1, then |x|2 so |x+1||x|+13. Then |x21|3|xc|. Let ϵ=1/2. Then if |xc|<ϵ/3, |x21|ϵ=1/2.

(b) |x21|<1/103 (I think there's a typo in my version - it says 1/103 but that is strange notation)

TBC

(c) |x21|<1/n
(d) |x31|<1/n

2Section 4.2

2.1Question 1

Trivial, not worth it

2.2Question 2

Soon

3Section 4.3

3.1Question 1

Prove Theorem 4.3.2

No thanks