Discussion:
Q: Corollary:(Divergence criterion for function limits).let f be a function defined on A, and let c be a limit piont of A. If there exist two sequences (x_n) and (y_n) in A with x_n not =c and y_n not =c and lim x_n=lim y_n=c but lim f(x_n) not = lim f(y_n), then we conclude that the functional limit lim f(x) as x->c does not exist.
use this corollary to show that each of the following limits does not exist.
a-lim Absolute value of x/x as x->0.
b-lim g(x) as x->1 where g is Dirichlet's function.