MATH100 December 2016
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 • Q9 (a) (i) • Q9 (a) (ii) • Q9 (a) (iii) • Q9 (b) (i) • Q9 (b) (ii) • Q9 (b) (iii) • Q9 (c) (i) • Q9 (c) (ii) • Q9 (c) (iii) • Q10 (a) • Q10 (b) • Q11 (a) • Q11 (b) • Q12 • Q13 (a) • Q13 (b) • Q14 (a) • Q14 (b) • Q2 (b) •
Question 06 (a)
Which of the following is the most general antiderivative of the function ? In the functions below, is an arbitrary constant.
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?
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The derivative of an antiderivative of a function should, by definition, be the original function.
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Note that . In other words, .
Recall that the anti-derivative of is a function satisfying . Also, for any constant , we have .
As a result, the most general anti-derivative of is
Remarks: one could also complete the question by taking the derivative of all the available anti-derivatives and checking if the result is equal to the original function (which for this question, may seem convenient because the answer is the first given anti-derivative), but this method may take more time, depending on the complexity and order of the given anti-derivatives.