MATH102 December 2012
• QA 1 • QA 2 • QA 3 • QB 1 • QB 2 • QB 3 • QB 4 • QB 5 • QB 6 • QC 1 • QC 2 • QC 3(a) • QC 3(b) • QC 3(c) • QC 4(a) • QC 4(b) • QC 4(c) • QC 51 • QC 52 •
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!
Assume the "if" statement of each answer choice is true. Then evaluate the limit to see if it matches the proposed conclusion.
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Let's test each answer one-by-one:
If n < 3, try a test value of n = 2. Then our limit becomes:
The answer does not match the conclusion L = 0 so this answer is not necessarily true.
- (b) If n = 3 then L = -2.
If n = 3 then our limit becomes:
The answer does not match the conclusion L = -2 so this answer is not true.
- (c) If n > 3 and n is odd then L =
If n > 3 and n is odd try a test value of n = 5. Then our limit becomes:
The answer does not match the conclusion , so this answer is not necessarily true.
- (d) If n > 3 and n is even then L = .
If n > 3, and even try a test value of n = 4. Then our limit becomes:
The answer matches the conclusion so this answer is correct.
The final answer is (d).
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