- Meaning of x → a: When the value of a variable x is brought very close to a number ‘a’ by increasing or decreasing its value, then it can be said that x tends to a. It is denoted by x → a.
- x → a means that value of x is very close to a but x ≠ a.
- Meaning of x → 0: If by decreasing the positive value of a variable x or by increasing the negative value of variable x, the value x is brought very close to ‘O’, then it can be said that x tends to ‘0’. It is denoted by x → 0.
- x → 0 means that the value of x is very close to ‘0’ but x ≠ 0.
When the value of a variable x is brought closer and closer to a number ‘a’, the value of function fix) approaches closer and closer to a definite number T, then we can say that as x tends to ‘a’ f(x) tends to T that is x a,f (x) —> l. This definite number T is called limit of a function f(x).
Symbolically it can be written as follows : \(\lim\limits_{x\to a}\,f(x)=l\)
l is the limit of f(x). Hence, f(x) ≠ Z.
