|
Past papers
All Maths department papers since 1992 are online here. The course has changed a small bit from last year and the year before but questions 1 and 3 from the 2004/5 paper and, from 2005/6, questions 2(a)(b)(d), 3 and 1(i) would be typical of the sort of questions I would like to ask. For question 1(ii) you are being asked to find the derivative from first principles, I would ask this question differently and I would ask it as a seperate question with three parts:
- (a) Without using l'Hopital, find the limit lim_{h\rightarrow 0}(sqrt{a+h}-\sqrt{a})/h. You might like recall (sqrt(A)-sqrt(B))(sqrt(A)+sqrt(B))=A-B.
- (b) Write down the definition of the derivative dy/dx in terms of a limit.
- (c) From the definition of the derivative, find the derivative of sqrt(x).