Science:Math Exam Resources/Courses/MATH103/April 2015/Question 02 (b)
• Q1 (a) (i) • Q1 (a) (ii) • Q1 (a) (iii) • Q1 (b) (i) • Q1 (b) (ii) • Q1 (b) (iii) • Q1 (c) (i) • Q1 (c) (ii) • Q1 (c) (iii) • Q1 (d) (i) • Q1 (d) (ii) • Q1 (e) (i) • Q1 (e) (ii) • Q1 (e) (iii) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) • Q8 • Q9 • Q10 (a) • Q10 (b) •
Question 02 (b) 

Consider the function and its series . Find and . (i.e. the 100th derivative of evaluated at ). 
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 

What is Maclaurin series for ? 
Hint 2 

In the Maclaurin series for , what's the relation between and ? 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Note that the Maclaurin series for is and the equality holds when .
Since is the coefficient of in the series and , we have when . On the other hand, has the following relation with :
Since (because 100 is not a multiple of 3), we have . Answer: 