0/0 in limit evaluation When evaluating limits we often come across the form 0/0 and we cant get a limiting value. As stated in many textbooks and online resources, the method to still get a limiting value as the input approaches a specific value is to first factorize or simplify the function to cancel out the factors/variables responsible for the form 0/0.
My question is doesn't it change the function altogether if we simplify it?
Because if we had used the original function it would not have been defined at that particular input? Can anyone provide the intuition or concept behind this?

The main thing is:

Taking the limit does not mean evaluating the expression at the point, but rather infinitely close to that point (i.e. approaching the point).

Simplifying an expression does change the behaviour at the point (for example getting a value where it previously was indeterminate because of division by 0 or something else), but it does not change the behaviour close to the point, i.e. as you approach the point, which is what matters for the limit.
