On 09/28/2013 11:30 AM, Hetware wrote: > I'm reading a 1953 edition of Thomas's Calculus and Analytic Geometry. > In it he states that given: > F(t) = (t^2-9)/(t-3) > > F(t) = (t-3)(t+3)/(t-3) = t+3 when t!=3. > > But F(t) is not defined at t=3 because it evaluates to 0/0. > > If someone were to ask me if (t^2-9)/(t-3) is defined when t=3, I would > say it is because it can be simplified to t+3. Am I (and/or Thomas) > engaging in meaningless hair-splitting regarding the question of F(3) > being defined?
I agree with Thomas. The two functions have the same values at all points except t=3, where the original is undefined, and the other has the value of 6.
The concept of "extraneous solutions" is closely related to this. -- Michael F. Stemper This post contains greater than 95% post-consumer bytes by weight.