Material Detail

Just a technic ,not a proof .

One of the students asked me if he could calculate lim sin(x)/x (x---> 0) by Hopital’s law as following. lim sin(x)/x (x---> 0) = lim (sin(x))’/(x)’ (x---> 0) = lim cos(x)/1 (x---> 0) = 1. I answered him “that is only a technic not a proof .To prove that derivative of sin(x) is equal to cos (x) ,it is necessary to know that lim sin(x)/x (x---> 0)=1,in other words in a logical ordering ,we can’t use Hopital’s law . Not only in this case but also generally we must be careful about logical ordering of mathematical predicates. ”

Disciplines:

• Mathematics and Statistics  / Mathematics  / Calculus  / Differential, One Variable