The #epsilon, delta#-definition can be used to formally prove a limit; however, it is not used to find the limit. Let us use the epsilon delta definition to prove the limit: #lim_{x to 2}(2x-3)=1#

Proof

For all #epsilon>0#, there exists #delta=epsilon/2>0# such that

#0<|x-2| < deltaRightarrow |x-2| < epsilon/2 Rightarrow 2|x-2|< epsilon#

#Rightarrow |2x-4| < epsilon Rightarrow|(2x-3)-1| < epsilon#

Hence, #lim_{x to 2}(2x-3)=1#.