Science:Math Exam Resources/Courses/MATH110/April 2017/Question 04 (b) (ii)
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Question 04 (b) (ii) |
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(b) Consider the function (ii) Find all vertical asymptotes of . |
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 |
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Recall that a line is a vertical asymptote of if either or are infinite. |
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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Solution 1 |
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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that is a vertical asymptote of if either one side of the limits, as or , of is infinite. When is given as a fraction form, a one side limit is infinite, then either the denominator goes to 0 or the numerator goes to infinity. Considering , the numerator approaches to , as , while the denominator goes to zero as . This shows that the possible candidates for vertical asymptotes are and .
Using , we have . This implies that is a vertical asymptote of .
Since the direct substitution gives , we use l'Hospital's rule to evaluate the limit; . which means that is also not a vertical asymptote. To summarize, the only vertical asymptote of is . |
Solution 2 |
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