Science:Math Exam Resources/Courses/MATH101/April 2018/Question 09 (i)
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Question 09 (i) 

Calculate the following limit: Hint: Maclaurin series will help you here. L’Hôpital’s rule will not.

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 

Take the Maclaurin series of the exponential function and the cosine function. 
Hint 2 

After taking the Maclaurin series you can cancel the highest common powers of from all the terms. 
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. Using the Maclaurin series for the exponential function and for the cosine function, we have and
Thus we have
Answer: The correct answer is . 