Technology

What types of technology can be used to teach limits in mathematics?

There are different technologies which have changed the whole arena of Mathematics. We can understand the concepts of Integration, derivation and limit by the help of technology. Especially the limit is going to be used in many areas of calculus, the l’hopital’s rule calculator

 will enable us to understand the concepts of Mathematics. Students need to understand there are two types of limits: finite and infinite. When students have learned the basic concepts of the limit, you need to understand. There are four types of the limit, the substitution, factorizing, rationalizing and LCD method. 

Students usually have no clue, when to use which method. But when they are using the limit calculator with steps, it help to determine, what is the appropriate method to solve the limit. When students are going to understand the basic concepts of the limit, when to implement which types of the limit. They can understand which types of the limit you are using whether it is finite or infinite limit. The other thing here is where to implement the substitution and where to implement the factoring method. This need to decide when solving the finite limits, the other thing when solving the infinite limit, how to implement the rationalizing and LCD method. The main thing here is to determine finding the conjugate,when solving the factoring method.

In this article, we are discussing the fact,how limits calculator assist us to solve the limit:

Technology and limit:

Now we are taking algebraic functions and using the lim calculator,how to solve the limit. When we are solving the limit solver by the online calculator. We need to implement the whole concepts on one algebraic function:

f(x) = x5x2-25x-5 

We are going to solve the limit by using the l’hopital’s rule calculator, and using two main methods to solve the limit of the following function: 

The First methodology:

Now consider the fact, we are implementing the technology in solving the limit:  

f(x) = x5x2-25x-5 

Now when we are using the technology, we can enter the values of the limit near to our approaching limit,which is “5” in this case. First we store the values of the limit in the limits calculator, then we can solve the limit by using the calculator.                                      

Step 1: First we add the values near to the approaching limit “5”, in this case we enter the value of 4.9999 on the home screen. Then you can press the Sto(Store) key. Then you need to press the Enter button, we are doing this by storing the data in the variable “x” of the l’hopital’s rule calculator.

Step 2: At the second step you are going to enter the value of the function in the limit calculator.

f(x) = x5x2-25x-5 

Step 3: When we are pressing the Enter button, then we are getting the result which is 9.9999. We are going to round the figure, and the answer of the limit would be “10”

You can observe, we are able to find the answer to the limit by using technology. It efficiently decided,we are going to implement the substitution method in the following limit. We have easily found the the 9.999, and the rounded answer of the limit is “10” . The  l’hopital’s rule calculator

 helping us to find the limit by using technology.  

The second methodology:      

In the second methodology, we are inserting a table to implement the technology in our calculations:

                                f(x) = x5x2-25x-5 

Step 1: We are going to use the graphing mode of the l’hopital’s rule calculator

, we first enter the values of the approaching limits like 4.998 and get the answer 9.998, and then  4.998 and get the values like  9.999. In this way we  can define our limit and resultant values. 

f(x) = x5x2-25x-5 

Step 2:  In the l’hopital’s rule calculator

, you are going to enter the incremental values “T”. In ths particular case,we can enter the values of the limit by increasing the 0.001.

          f(x) = x5x2-25x-5  We are entering the values of the limit from 4.998 to 5.003 and incrementing the values by T” by 0.001 and getting values of the table as follows:

Step 3: When we enter the table option,we get the values of the approaching limit “X” and the result of the  “Y”.

             X                                 Y

           4.998                                9.998

           4.999                                9.999

           5                                       Error

           5.001                               10.001

           5.002                               10.002

           5.003                               10.003

The first values we entered is “ 4.998” and the resultant limit is “ 9.998. Then entered the value limit “4.999” and got the value which is “9.999”. Then we entered “5” and the l’hopital’s rule calculator

 showing an error message. It means when we are entering the value of the “5” in the denominator, we are getting unsolvable limit.

      f(x) = x5x2-25x-5

You can observe the limits calculator has made the concepts of the limit easy for us. We can solve it by using the simple command of the  limit solve technology. We can’t solve the close approaching limits to the table. The limit calculator with steps also made it easy to understand the procedure.

Footnotes:

The concepts like limits are the basic concepts of calculus, we need to create a complete understanding of the concepts. We need to implement it to the derivations and the integration. When we are using technology, we are able to create the basic understanding of the concept. Technology like l’hopital’s rule calculator

, integration calculator, and derivations calculator  are grealthy helpful in creating the understanding of the concepts and solution of these concepts. This is essential in today’s digital world, to use the technology in solving the length questions of the calculus. You can also find online help, how to use these tools online.

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