Science:Math Exam Resources/Courses/MATH110/December 2017/Question 03 (a)
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Question 03 (a) 

Evaluate the following limits or determine they are either infinite or do not exist. (a) 
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 

One can plug in values to a limit provided the function is continuous. 
Hint 2 

A power function is continuous, whenever it is defined. 
Hint 3 

Strictly speaking, the limit means as opposed to However, these two are equivalent since the constant function is continuous and has limit (trivially!) when . So one of these limits exist if and only if the other is, and are equal provided either exists. In other words, there is no ambiguity in these two possible interpretations.

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. By the rule of exponents, one can rewrite Since the power function is continuous at the point , we have Therefore, Answer: . 