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Monday, 3 March 2014

Limit of a Function

 


A function   f(x)  is said to tend to the limit   l   as   x  tends to   a   from the right

if given element is >0  there exists a number

delta>0  , such that ;

/f(x)-l/< of that element 

whenever , a<x<a+delta .

This number   l  is called the right 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 tend to the limit   l  from the right if  f(x)  tends to   l   as   approaches   through value of   x   greater then  a .

working rule for finding the limit from the right at  x=a.

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

b)  --    h-->0  in   f(a+h).