The function f:R-{0}→R given by f(x)=1x-2e2x-1 can be made continuous at x=0 by  defining f(0) as

:−     f0=Ltx→0  1x−2e2x−1=Ltx→0 e2x−1−2xxe2x−1                                      =Ltx→0 2e2x−2e2x−1+x.2e2x                                      =Ltx→0  4e2x2e2x+2e2x+2xe2x                                      =42+2=1