Science:Math Exam Resources/Courses/MATH103/April 2015/Question 01 (a) (iii)
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Question 01 (a) (iii) 

Given the following general terms determine whether the corresponding sequences are converging, diverging, and/or bounded. (do not calculate the limit of converging sequences.)
(iii) 
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 

Recall that are exponential functions because the variable sits in the exponent whereas are power functions. So when , which function in the numerator and the denominator is dominant? 
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. By the Hint, in the numerator between and , the exponential function becomes much larger as . Similarly, in the denominator wins when becomes large, thus we have when . Now note that so and therefore,
