Limits from the Left

 


A function   f(x)   is said to tend to the limit   l'   as    x    tends to    alfa    from the left

if given element is > 0

there exists a number   delta>0 

such that;    /f(x)-l'/<of an element

whenever ;   a-delta<x<a  .

This number   l'  is called the left  hand limit of 

 f(x)  at   x=a   and it is denoted by ;

lim x-->a  f(x)=l'  or  lim x-->a-0 f(x)=l'

or ;  lim h-->0  f(a-h)=l'

This limit is also written as   f(a-0)

In simple words ,  f(x)  is said to tend to the limit   l'  from the left if    f(x)  tends to   l'  as   x  approaches   a   through values of   x   smaller then   a .

Working Rule for finding the limit from the left at

x=a 

A)  Put   a-h  for   x  in  f(x)   to get   f(a-h)

B)  Make   h-->0  in  f(a-h) .