look...........if u ask the question like that............if x=5 then....tell............

 

what is the value of expression..........

 

               x²   -   5x 

           ---------------

                x    -   5     

then u will put x=5................

and the answer will be................

                25    -     25

               --------------

                 5      -    5

 

                    0

                  ------

                   0

then what u will do.............

therfore we think that x  is tending to 5.............not exactly 5.................ok

now look

 

                     x²     -    5x

  lim             ----------------

 x->5                 x     -    5

 

then    u will do..............differentiation and then u can do it...............or

                      x    (   x   -    5 )

 lim              ----------------------

x->5                 ( x     -     5)

 

as x  is not equal to 5...............but tending to 5..............so we can cancel x-5.......from both numerator and denominator............

we get

 

expression               =     x   = 5..............

 

understood......why this theorem was developed?......

if not please nudge me....

thanku