Wednesday, 5 March 2014

Limit of f(x) at x=a


A function   f(x)  is said to tend to the limit   l   at   x=a  

if given   element>0  there exists a number  delta>0

such that ;  /f(x)-l/< that element 

whenever ; /x-a/<delta 

In simple words ,   f(x)  is said to tends to the

limit l  at  x=a 

if   f(x)  tends to  as  x  approaches  a  

through values of  x    greater then  

as well as   values of  smaller than  a.

The limit l  of  f(x)  at  x=a  denoted by

lim x-->a  f(x)=l

It is clear from above that

f(x)  tends to the limit  at  x=a  implies .

lim x-->a+0  f(x) = lim x-->a-0  f(x) 

=lim x-->a  f(x) = l

provided both the right-hand and left-hand limits exists for

x=a  .

If the domain of definition of   f(x)  is

[a, b] , then existence of

lim x-->a+0  f(x)   does not arise .

Similarly the question of existence

 lim x-->b+0  f(x)   also does not arise .

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