Just discuss an easy AL Applied Mathematics (II) Question with students.
Let be twice differentiable functions such that .
(a) Let , where . Show that .
(b) Using (a), or otherwise, find Taylor’s expansion of the function about , up to the term in .
In answering (a), can be written as
The usual practice, differentiate w.r.t. , obtaining
A student, Fu, queried that when the term is a constant (i.e. cancel ), the step of putting into may not be zero! Good question!
Friends, is it necessary to worry about it?