Wednesday, 5 March 2014

Limits from the Left

 


A function   f(x)   is said to tend to the limit   l'   as      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   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) .



No comments:

Post a Comment

Our Latest Post

How to Evaluate an Integral

In this video you will see how to evaluate an Integral. This video shows an example, by this example you will see about how to evaluate an ...

Popular Post