Science:Math Exam Resources/Courses/MATH102/December 2013/Question B 05
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Question B 05 

Compute the limit

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 

A shortcut solution is obtained by noticing that this is the definition of the derivative for a certain function at . What is this function? 
Hint 2 

We could also solve this by multiplying the numerator and the denominator by the conjugate of the numerator, i.e., . 
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 1 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Recall that the definition of the derivative of a function f at x is Following hint 1, we see that if and , then 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The slower solution uses hint 2 and multiplies the numerator and the denominator by the conjugate of the numerator
