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 |x−1| that will ensure that
(a) |x2−1|<1/2
|x2−1|=|x−1||x+1|. If |x−1|<1, then |x|≤2 so |x+1|≤|x|+1≤3. Then |x2−1|≤3|x−c|. Let ϵ=1/2. Then if |x−c|<ϵ/3, |x2−1|≤ϵ=1/2.
(b) |x2−1|<1/103 (I think there's a typo in my version - it says 1/10−3 but that is strange notation)
TBC
(c) |x2−1|<1/n
(d) |x3−1|<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