The definition of starts with "For every , ...". Substitute, say, (or any concrete that is less than ) and see what the rest of the definition says.
Aha I see,but why its not correct to choose L - A? ;
0<|x-a|<dlta ====> |F(x)- L|< e
by |y|<m >> -m<y<m
We get ; -e<F(x)-L<e
Now e=L -A
so ==> F(x) - L > -e = -(L -A)=A - L
/ + (-L)
===> F(x)>A- L + L = A ==> F(x)> A!
Not correct ?(it is given that L -A >0,so the value of e is positive! and it fits with the requirements! )
Thank you