Science:Math Exam Resources/Courses/MATH307/December 2010/Question 01 (d)
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Question 01 (d) 

Let 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? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The previous part should help deduce that we want to look for values of a in three regions given by

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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 :
So, the sketch looks like this: 