In Calculus, limit of a function is an important concept and it is use to know the behavior of the function near any definite input. Limits have many applications in the mathematics. A limit tells how a function comes close to a certain value, and is used to get the value of that function.
Let’s see the general notation of limits of Functions.
: lim x→c f(x) =L,
Where, L is the limit of function f(x) as function value (x) approaches other constant value c. When value of function x is closed to constant value c then function f(x) becomes close to limit of L. If there is no other value for this function then function is within same condition, like notation given below:
lim x→c f(x) =L,
Or f(x) → L as x → c,
The definition of a limits is not concerned with value of function of f(x) when function value x is equal to constant value c. So all we care about the values of the function f(x), when x is close to c, on either the left side or right side .
Limit Functions are also following the constant rule which is useful for working with and computing limits in this rule function f(x) is constant for all function value x then the limits as x approaches constant value c must be equal to constant value b. It means limit of function is
lim x→c b =b.
Definition of Limits of a function (Definite form)Back to Top
Limits of a function, can be defined as the approaching value of the function near a given input. Let’s take a function 'f' which, has the output f(x) to every input 'x' and the function has limit 'L' and an input 'p'. f(x) is close to 'L' , when f(x) is close to 'p'.
Limit of a function evaluation ( indeterminate form )Back to Top
Whenever we deal with limits we have to compare Numbers and Functions and after that we need the knowledge of limits and its indeterminate forms. In limits the indeterminate form is defined as an algebraic expression. Limits Indeterminate forms, means any form which can't be precisely determined or which doesn't possess a definite solution. The Limits indeterminate forms includes various Functions or numbers like: