MATH110 December 2017
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) (i) • Q8 (b) (ii) • Q9 • Q10 (a) • Q10 (b) •
Question 03 (c)
Evaluate the following limits or determine they are either infinite or do not exist.
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!
What are the limits of the numerator and denominator, respectively?
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Let and . Note that and are polynomials and hence continuous everywhere. Following the Hint, we compute
For close enough to , we get divided by a very small number. Therefore,
Notice that the negative sign comes from the . The sign of is positive near because is close to .