Limit and Continuity:

Suppose the function. Obviously f(x) is not described at x = 1. At x = 1, , which is meaningless.

 From the above table it is obvious that as x approaches to 1 i.e. x -> 1 from the left hand side (denotes x approaches 1 from the values less than 1)f(x) approaches to 2 i.e. f(x)->2. The number 2 is known as the left limit of f(x) and in symbol we can write  

Again let us take the nature of f(x) where x approaches tends to 1 from the right-hand side.

It is obvious from the table that as x approaches to 2 i.e. x -> 2, from the right-hand side (denotes x approaches 1 from the values bigger than 1) f(x) approaches to 2 i.e. f(x) -> 2. Here 2 is known as the right-hand limit of f(x) and in symbol we can write

Therefore we may see that f(x) is not given at x = 1 but its right-hand limit and left-hand limit as x -> 1 exist and are same. When  are same we can say  exist and is similar to 2.

Meaning of (x -> a)

Suppose x be a variable and 'a' be a constant. x consider value closer and nearer to 'a', then we may say 'x towards to a' and write 'x -> a' and it doesn't define x = a.

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