Hi I’m Hari Prasad let us start the chapter limits in this chapter we are going to learn how to find out the limit of the function and what do we mean by limit of a function let us start module number one in this particular module we are going to learn what is the meaning of the word tending to let us start the chapter now meaning of X x tends a is what we have to learn first so immediately the question that comes to my mind is what is the meaning of X tending 2 or X tending to any particular number a in general so it can be particularly X tending to 2, X tending 3 something like that so what is the meaning of that does it mean x is equal 2 does it mean know that x is equal to something else so answer this particular question will consider the following example consider boy who always covers fifty percent of the total distance that means the boy covers five meter for the first time so where he will be he’ll be at five meter mark the boy will cover all fifty percent of the remaining five meter that means he will cover all 2.5 meter for the second time third time he will cover 1.25 meter and so on if this is the case when the boy will be exactly on 10 meter mark can you predict the answer is the boy will be never on 10 meter mark but he’s very close to 10 meter mark right similarly when we write X tending 2 we mean that X is very close to two but it is not equal 2 consider the number line we have minus 1 0 1 2 3 and so on when x tends 2 to it can be close to two when I say close to two it can be from the left side or it can be from the right side also write suppose if I say x tends 2 and if X’s or close to 2 from the left side then it can take the following values can you get what are the values it can take x is equal to 1 .8 is possible it can take 1.9 yes it is close to 2 ,1.99 yes it can take these values right and one point nine nine nine yeah still very close to 2 and so on there are many infinitely many values that it can take but when X tends to 2 if X is close to two on the right then it can take the following values which are the values can you guess the point 2.8 can take it can take 2.2 it can take 2.1 and 2.01 so on it can take many other values right is so now the question is clear to us let us now talk in case of general elements like X and a, let X be a variable is the meaning of variable quantity which keeps changing and a be a constant with the meaning of constant quantity which has a fixed value right if X takes the value near Nearer to a then we say that e tendens to a and we write it as X arrow mark a We write it as does x tends to a note that in this case X cannot be equal to A and we are not specifying any manner in which X should approach a that means it can approach to a from left as well as it can approach from right now when X tends to a from the left we have the following situation if X approaches a taking all values less than a but Nearer to a then we say that extends to a from the left we write this as extends to a and we put a small minus over a this minus is not to be used in any of the calculation similarly when X tends to a from the right we have the following situation if X approaches a taking all the values greater than a but nearer to you a then we say that x tends to a from the right and rewrite it as x tends to a plus we write small plus sign over a like this is the notation that you need to remember thank you.

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