1)Given a function defined on [a,b], we say it is null iff INT(a,b) f^2(x) dx=0.
Note, f(x)=0 is null on any interval however the converse is not true.
Show that if g(x) is any function defined on [a,b] and f(x) is a null function then,
INT(a,b)g(x)f(x) dx=0

2)Show that the diameter is the longest chord. (Not necessarily hard I want to see how many reasons you can come up with).

3)Let a,b be positive integers. Given necessary and sufficient conditions so that,
(ab)/(a+b)
Is a positive integer.

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