Limit concepts
Concept of limit in mathematics
Introduction:
The concept of the limit is very important in mathematics and other natural science. In the 17^{th} century it was firstly introduced by two great physicists and mathematicians Sir Isaac Newton and G.W. Leibnitz. The great physicist Sir Isaac Newton used the concept of the limit or calculus to define the study the motion of the body. The concept of the limit and calculus are widely used in different fields.
Limit:
Limit is the mathematical concept that defines the value of a certain function relative to certain nearby values. Hence it is the value of that function which approaches as some index approaches.
To understand the concept of the limit, let us consider the function
Now we try to understand the behavior of the given function at different values of the x.
When we put x=4 then clearly function which has no meaning. It means we cannot define the function when the value of the x is equal to 4.
Now let observe some cases applying the approach value of 4 then we obtain the following result.
Value of x |
F(x) |
x=3.9 |
f(x)=7.9 |
x=3.99 |
f(x)=7.99 |
x=3.999 |
f(x)=7.999 |
x=3.9999 |
f(x)=7.9999 |
From above it is observed that as the value of the x approaches to 3 then the value of the given function approaches to 8.
Mathematically this can be written as x→4 then fx→8 and written as
where the symbol right arrow defined the approach and lim defined the limit. From the above explanation, the limit can be defined as the approaches value of given function as the index or input value approached certain limiting values.
The indeterminant firm of the limit
Let any function f(x) is said to be indeterminant firm at any value of x=a when function yield
such indeterminant firms are meaningless and can not be defined at all.
Few properties of the limit:
Let us consider any two function and and any constant c then we have
Some important expansion
This expansion is used to prove some important theorem of the limit which has given in the upcoming section.
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- Edubomb
- SOURCS
- Author G.B. Budhathoki
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