Note that in problem 2, <x,l_1> = l_1(x), etc
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the differentiation and integration operators are linear
the squaring operation is not linear, and neither is the integral of the square of f(t)
// take int_a^b to mean the integral from a to b //
then int_0^1 t^2 f(t) is a linear functional, since f is unaffected
int_1^2 f(t^2) dt = int_1^4 f(u) du which is ...
Linear Functionals, Continuous Derivatives, Vector Spaces and Scalars are investigated.