Limits Day 2

In the earlier videos and exercises you saw how to find the limits from a graph(plotted readily) with identified undefined values or a different defined value.It was easy to see the approach from below and above a value (say 'a') and declare if the limits were same  if so if it was also the same as f(a).
of the other methods when a graph is not given but a expression (formula of the graph ) is given then  you have to find the limits by algebra...

Video 4.Limits by substitution

Video 5 Limits by factorisation

video 6 Limits by conjugate

Find limits (substitution or by factorisation)
Tip:At times you will find the denominator and the numerator both become "0" on substitution,then you should try factorization. If  by substituting ,for example x=a, results in 0/0,then you know by reminder theorem in algebra,that '(x-a)' must be a factor in numerator and denominator.Using this (x-a) as a factor,you can get the other factors of the Numerator and Denominator.