Mathematics 1560 Lecture Notes - Lecture 2: Quotient Rule, Product Rule, Power Rule
Document Summary
We have to be careful in our dealings with functions! Notice that f (x) = and g(x) = x are not the same functions! They x(x 1) x 1 do not even have the same domains. Therefore we cannot in general say x(x 1) x 1 functions. However, this equality holds if x lies in the domains of the x(x 1) x 1. We can also say f (x) = g(x) if x 6= 1. If f (x) gets arbitrarily close to l for all x su ciently close to x0, we say that f approaches the limit l as x approaches x0, and we write f (x) = l. limx x0. The above de nition is informal (that is, it is not mathematically rigorous) since the terms arbitrarily close and su ciently close are not de ned. Evaluate lim x 1 f (x) = lim x 1. From above, we see that x(x 1) x 1.
