Articles

Here are some real life applications of limits

by James Johnson Teacher / Writer

Ever heard of limits? No these are not those limits or restrictions that we know in general, these are the limits of calculus. The calculus students would be quite familiar with this term. 

Now, for the beginners a limit is an integral part of calculus and it is defined as the value approached by a function or sequence as the index or input reaches close to some value.

Integral solver is an important concept in math and students must learn integration in order to top the exams. There are several integration calculators which one can find online for learning & practice. 

A limit is usually expressed as: 

 Image result for limit expressed as

In this notation as x approaches a number c, the function f(x) gets closer to L.

Now, let’s get to the applications of this calculus tool in daily life. Limits are not just restricted to calculus operations to define derivatives and integrals, but they also have a broad range of practical utility in physical sciences.

Examples of limits:

For instance, measuring the temperature of an ice cube sunk in a warm glass of water is a limit. Other examples, like measuring the strength of an electric, magnetic or gravitational field.

The real life limits are used any time, a real world application approaches a steady solution. One example of a limit is a chemical reaction started in a beaker in which two different compounds react to form a new compound. Now as time approaches infinity, the quantity of the new compound formed is a limit.

In the case of limits , when we relate it to infinity it means how the numbers behave as they are getting larger or a series, where new numbers are continuously added.

One of the major utilities of infinite limits is that it allows us to consider large complex functions and let us figure out which pieces of information are relevant. In other words it let us know, the part of information that contributes the most towards the answers. This allows us to simplify problems to solve them easily.

 

                                   

In the picture above, the artist mixes the limits between real life and the smartphone. Here, the artist approaches some degree of closeness to reality.

For a better understanding let’s just keep it simple. The simple example of limit is when we measure something, for instance, we measure the length of an object or a line drawn with a device such as a scale. Suppose the length was 20 cm but are we sure our measurement is exact, it may be 19.899 or it may be 20.011.

We get really close to measuring something with a device, if we are careful but we cannot achieve the exact measure. To declare something at a limit 20.014, we need a sequence of related measurements.

The concept of limit is important to recognize the real number system and its diverse attributes. In one view real numbers can be described as the numbers related to the limits of convergent sequences of rational numbers. 

One concept is a derivative, it is a rate of change, and can be estimated based on limits .The limits are also vital for computing integrals (also called area expressions). This computes the complete area of a section by adding the sequence of infinite numbers divided into small parts. 

These are some of the real world examples of the limits. Yet, it has a wide range of practical significance, which makes its calculation important to us. Now, how do we calculate it? 

There are many ways like including the x value, by factoring etc. but the easy way out is to use an online tool. One such tool is an online limit calculator, an easy to use device available online. Just put the values of function and the value of limit to calculate it. Good luck!


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About James Johnson Freshman   Teacher / Writer

8 connections, 0 recommendations, 26 honor points.
Joined APSense since, January 8th, 2020, From Birmingham, Al, USA, United States.

Created on Apr 19th 2020 09:47. Viewed 789 times.

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