CBSE Class 11-science Answered

Since the value of x will never actually become 2 while the limit is 'on' , (x -2 ) will never actually become equal to zero.

Also the expression takes the form 0/0 if you substitute x=2.This is an indeterminate form, which means that the answer of 0/0 can't be determined..

The culprit is the value of x as 2.

 Hence we should try to eliminate the factor (x-2) forrm both numerator and denominator.It can be easily cancelled as it's a non zero value.

Once the 'culprit' i.e. the term which takes the expression to the indeterminate form, is removed , then  we are free to put x=2.

 Only at this stage we  should not write lim x tends to 2.

 Hope this clears your doubt.