Hetware wrote: > [...] I was attempting to understand why it seemed > possible to simply assume the function to be continuous at t=3, and then > treat it as f(t) = (t^2-9)/(t-3) = t+3. The problem was that I was > assuming more about the function than is given by the definition f(t) = > (t^2-9)/(t-3).
Why don't you try to prove (in all the gory epsilon-delta detail) that f is continuous at t? You will find that f is continuous at every t bar 3, and that the definition of continuity cannot be applied at t = 3 because f(3) = 0/0 and I bet you were taught at school that 0/0 is undefined. So the attempted proof comes to a halt.
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg