Science:Math Exam Resources/Courses/MATH100/December 2014/Question 08 (c)
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Question 08 (c) 

Let . Note is the natural logarithmic function, also denoted (c) Find the horizontal asymptotes of the graph , if they exist. Justify your answer. 
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 

What behaviour defines a horizontal asymptote? Is there a rule that can help with indeterminate forms? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since the function is only defined for , we need only consider . Since we use L`Hospital's rule to obtain
So the only horizontal asymptote is . 