Appendix for Chapter 3: A
TUESDAY 8 JUNE 1993
14:00-14:30 Lona-Jay
sequences and series exam questions. They are dealing with the convergence of Sxn/n!
L: . . let's use the ratio test.
they write the expression xn+1/(n+1)!/xn/n!
she: what should I write here?
J: (hesitant) .. the || of that.
she: yes, so I can be sure it's positive...
... so the convergence is proved
The next part or the question implies the use of the term by-term-differentiation theorem
she: this is a theorem that comes up every year in the exam in some form.
By the way this exam question gives them the opportunity to decide the differentiability of ex only by stating('precisely')known theorems.
[it is the kind of formulation of an exam question that gives me the impression that the person who set it had a particular solution in mind and having that they tried to pose the question without 'betraying' its secret]
J: ... so ex=
S ...J stops and thinks from where to sum... L says from 1.she: yes, you can try to differentiate the first term and see what happens to it.
Then with the help of L she writes down ex=
S ...= ex and they go on with the next part of the question where an fc is given and they have to prove that its derivative is zero. Silence.she: you can do that can't you? Just differentiate! [did they expect something trickier? why didn't they answer such a simple question?]
.... she writes it down...
[she writes also a query for later... see below]
she: so if its derivative is zero then the function is...
[typical way of her teaching: unfinished sentences, waiting for the students to complete them]
L:. . .constant
she: and how do you find which constant is it? L:...let's try a couple of values for x.
she: and which value is obvious to try? L:...Zero
they try it and then she says:'it is a constant so you only need to evaluate at one point'
Now she writes down ex
she: what do you know about it?
[in an hysteron-proteron way she solves the query previously established -it was about positive and negative x]
she: ... not many people would be bothered about it