If all your class fellows come to school using the same school bus, does that mean all of you are picked up from the same pick up point or are you all gathering at one class fellow’s home to picked up?  No, not at all obviously. All of you belong to different places in the city and have different routes for the school. But you all have to go or gather at the same destination, your school.

It’s like the merging of different subjects to one single destination. In mathematics, it is an example of limits. As at a particular value the conjunction of a function occurs. The way how functions are constraining may express by limits.

The concept of functions has around for centuries, however the definition of limit known and understood by us has formulated in the late 19th century. It has recorded that to find an improved approximation of the circle’s area the ancient mathematicians utilized the concepts of limit.

In order to understand and acquire useful information regarding limits and quadratic formulas go through this article.


Mathematically, when some value is approached by the input, the value approached by a function in response is called as a limit. Limit is an important concept utilized in Maths as well as Calculus to define the derivatives, integrals and continuity. In fact, these two broad concepts, derivatives and integrals are based on the foundation concepts of limit.

Continuity and limits are interrelated to each other, however the functions could be continuous or discontinuous in limits. There should be small changes in the output if there are small changes in the input, this is how we define a function’s continuity.  

The local behavior of functions close to the points of interest is also analyzed by implementing the concept of limit. In cases when the variable approaches its limit through values minor than the limit and the other variable approaches its limit through values bigger than the limit, then a right and left-hand limit occurs and limit isn’t defined.

We may also approach our limits by using online multivariable limits calculator.

Limit Laws

The value of the function approaches when the variable approaches its limit from the right is the right-hand limit of a function. Whereas the value of the function approaches when the variable approaches its limit from the left is the left hand limit of a function.

Constant Law

Sum Law

Difference Law

Constant Multiple Law

Product Law

Quotient Law

Special Limit

Power Law

Power Special Limit

Root Law

Root Special Limit


Limits also have practical approaches and implications in various disciplines of physical sciences; it isn’t limited to just calculus in defining integrals and derivatives.

Integral and derivative are two main pillars of calculus building. No doubt these are complex but also the major part of calculus that are based on limits. Derivative and integral contains complex calculation. But modern technology provide us great online tools like integral calculator by parts that helps students as well as teacher for solving such type of problems very easily and within an instance of time.

For example, to measure an ice cube’s temperature dipped in a glass of warm water. Moreover, to measure the strengths of gravitational, magnetic and electrical fields.

Related: Also Learn the Applications of Derivatives.

Another example includes the chemical reaction occurring by the combining of two different compounds, and as a result the formation of  a new compound is called the limit. When we talk of limits and infinity, we’re talking about how numbers work as they get greater or a sequence of numbers.



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