Science:Math Exam Resources/Courses/MATH100/December 2015/Question 10 (c)
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Question 10 (c) 

Let . (c) Find the horizontal asymptotes of the function (if they 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

If or , then the horizontal line is a horizontal asymptote of the function. 
Hint 2 

How does the exponential function behave when ? 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. As , the rate at which the exponential function decays to zero is much faster than the rate at which the two linear functions and grow; therefore More rigorously, we can apply l'Hospital's rule twice to compute that
