your question's answer involves the basic concept of limits. limits are used when a function has a discontinuity at some point and it cannot be evaluated at that point by directly plugging in any value in the domain. take for example lim x->2(x^2-4)/(x-2).here if we simply put the limit we get an undefined expression. instead if we cancel out the factors we get a definite value. another important point is that when a function is said to have a limit it means that at the neighbourhood of that point (however close be the neighbourhood points doesnot matter because by definition of limit the fuction only approaches that point and not gets it)the function is defined. it would be good if we consult a textbook once again.