The topic of limits in calculus is important only upto the stage of start of differential calculus.Thereafter it looses its utility in most of calculus.It appears briefly in definite integrals and thereafter in Series(AP BC) .But the concept is the most important stepping stone for entry into the subject of calculus.The concept of limit is the one that enable one to examine microscopically at the behavior of functions, which otherwise seem to be just expressions .It enables you to examine as if you are looking at an atomic particle inside a molecule just by applying simple mathematical tools (learnt in 9th grade level algebra-geometry-trigonometry)
First Blast
Study the videos below-pause and replay if you did not understand some thing-and try to answer the following questions.
You will notice that the video discusses about a function f(x) or may be g(x), and adresses a problem that arises when"x"=some value...
Explain the reason for "the gap".
How does the limt concept overcomes the 'gap problem'?
First Lessons
Right through the limits chapter and its problems,one fact that can be easily overlooked and make you stumble is that limit is not the same as substituting for 'x' in f(x).....though in some situations you can find it by substitution. Later you will learn the truth about it and to be watchful.Its for this reason the videos talk about approaching a value and not substituting the value.
Below is Simple intro using a st line function - graph.(DON'Tgo to other videos on the sides-they will come later and will confuse you now)
You should pay attention to the symbolic way of expressing limit(from left hand side and right hand side)-they can easily confuse you when solving a problem and potential error causing symbols.Try to understand the difference between the approaching a limit value from a negative side and the positive side (I say in my mind -as from below the value and above the value...that reduces errors).Later you will do lots of problems involving the side of approach.
Clear all doubts before watching next viseo.Keep a paper pencil for any scratch work.
video 3. Exercises-Limits from graph
Study the problem below and check answers.
Exercise
Study the problem below and check answers.
Exercise
1. Below is the graph of 
(a) 
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