Science:Math Exam Resources/Courses/MATH102/December 2011/Question 02 (a) ii
• Q1 (a) i • Q1 (a) ii • Q1 (b) i • Q1 (b) ii • Q1 (b) iii • Q1 (c) • Q2 (a) i • Q2 (a) ii • Q2 (a) iii • Q2 (b) i • Q2 (b) ii • Q2 (b) iii • Q2 (c) • Q3 • Q4 (i) • Q4 (ii) • Q4 (iii) • Q4 (iv) • Q4 (v) • Q4 (vi) • Q5 • Q6 • Q7 (i) • Q7 (ii) • Q7 (iii) • Q8 (i) • Q8 (ii) • Q8 (iii) • Q9 •
Question 02 (a) ii 

ShortAnswer Problems. A correct answer in the box gives full marks. For partial marks work needs to be shown. Note: If a limit does not exist, indicate whether it approaches or . Find the limit 
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 

Why does plugging in into the fraction not work? Maybe some factoring can help here. 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Notice that we cannot simply plug in as we will get , an indeterminate form. To evaluate this limit, factor the numerator and denominator of the fraction as much as possible: Notice that there is a term that can be cancelled out from the numerator and denominator and rewrite the limit: Using the properties of limits, we can now evaluate this limit by plugging in the value 