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Question 3 (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.
The key is to bring an x out of the square root: .
Here |x| denotes the absolute value of x. Since x is negative, |x|= -x .
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.
Denote the limit by L . Then,
Since x is negative, |x|= -x , thus
The limit of the numerator is 5, while the denominator is converging to 0 from above, because for very negative values of x we have 1 + 3/x + 2/x^2 < 1. Therefore, the limit diverges to positive infinity.