A function

*is said to tend to the*

**f(x)***at*

**limit l**

**x=a**if given

*there exists a number*

**element>0**

**delta>0**such that ;

**/f(x)-l/< that element**whenever ;

**/x-a/<delta**In simple words ,

*is said to tends to the*

**f(x)***at*

**limit l**

**x=a**if

*tends to*

**f(x)***as*

**l***approaches*

**x**

**a**through values of

*greater then*

**x**

**a**as well as values of

*smaller than*

**x**

**a.**The

*of*

**limit l***at*

**f(x)***denoted by*

**x=a**

**lim x-->a f(x)=l**It is clear from above that

*tends to the*

**f(x)***at*

**limit****l***implies .*

**x=a**

**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

*is*

**f(x)***, then existence of*

**[a, b]***does not arise .*

**lim x-->a+0 f(x)**Similarly the question of existence

*also does not arise .*

**lim x-->b+0 f(x)**