MATH307 December 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) • Q6 (f) • Q7 (a) • Q7 (b) • Q7 (c) •
Question 01 (d)
where a is a real number.
(d) Sketch a graph of cond(A) as a function of a for -∞ < a < ∞
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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The previous part should help deduce that we want to look for values of a in three regions given by
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For convenience, let's recall our results from part (b) and part(c):
and cond(A) is not defined when a = 0. This suggests considering three cases for :
- Case 1: If then
- Case 2: If then
- Case 3: If then
So, the sketch looks like this:
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