Limits in Calculus

How to Teach the Concepts of Limits Using Advanced Technology

In our time, concepts of Math have totally changed by technology and online tools like the limit calculator. The Students and learners are utilizing technology to learn the difficult concepts. How to teach the concepts of limits using advanced technology.

Teaching Limits with Technology

Concepts like derivatives, integrals, and limits in calculus are difficult to understand but when you are using the limits calculator it becomes easy for the students. New technology influencing learning make it easier for the students to learn that there are two types of limits.

The infinite and the finite limit. We are using the four methods to solve the limit questions: the Substitution, the Factoring, the Rationalizing and the LCD or the Least common denominator method.

It can be just too tricky for the students to learn which method is best to solve the limit. The limit calc with steps makes the whole concept of the limit just too easy for the students.

Methods with the Limit Calculator

The limit calculator automatically decides which method is best to solve the limit question and how we are going to implement it to the question. The limit solver is self sufficient to find which method is the best to solve the question of the limit.

There are four basic methods to solve the limit by the  calculator:

  • The Substitution method of limit
  • The Factoring  method of limit
  • The Rationalize method of limit
  • The LCD method of limit

Technology to Solve the Limit Calculation

We are highlighting and  teaching the concepts of limits in mathematics  by using advanced technology like the calculator . We are solving an algebraic function, to understand the concept of the limit.

 

 

We are going to use the  lim calculator, to solve the limit. The limit solver is used to solve the limit  there are two types of method.

First Methodology to Solve for a Limit

Step 1: For solving the limit enter the approaching limit in the calculator. In this case the closest to “5” and we are entering the approaching number is 4.9999 on the screen of the limit calc with steps. Just Press the Sto (Store) Key to enter the value of the limit in the calculator.

After that you need to press the Enter button to store the values of the approaching limit 4.9999 into the “x”.  The values are  processed by the calculator of 4.9999 and then providing the output  of the limit.

 Step 2: You are entering  the values of the given function in the limit calc in the second step. We are actually entering the limit value in the second step to get the output values.

Step 3:  Press the Enter button to get the output result which is our answer solved by the  calculator. The result is 9.9999 which is represented by our online tool. The  rounded figure of  the 9.9999  would become “10”.

The  calculator also solves the limit of  4.9998, and we get the resulting value which is  9.9998. When we are  entering “5”, the limit calc will show an error message, as it makes the limit unsolvable.

Second Method to Solve for a Limit

We are drawing a table to solve the limit by the second methodology to solve the limit by the limit calc.

Step 1: In this method we are presenting the graphing method to solve the limit by the algebraic method:

 

 

Step 2:  Enter the values of the incremental values “∆T” in the  calculator to solve the limit .We need to enter the  incremental value is “∆T” 0.001.The  incremental values  to the limit in limit calc with steps. These values generate  a table of the input values of the limit and output values. This is actually the solution of the limit.

We are entering  the values up to 4.998 in the calculator.

X                                 Y
4.998                                9.998

4.999                                9.999

5                                       Error

5.001                               10.001

5.002                               10.002

5.003                               10.003

Step 3:  The input limit to the calculator is 4.9998 and the output result is 9.998. When  we are entering the values of 4.9999 we are getting an output value of  9.999. When we are entering the value of 5, we are getting an error message, it means the limit is unsolved at this point.

Entering the values of 5.001 we are getting output value of  10.001of our limit by the calculator .Entering the values of 5.002 we are finding out put value of 10.002. Entering the values of 5.003 we are finding out the value of 10.003.

The rounded answer is “10” . This is represented by the limit calc.

Teaching Limits with Technology

There are many factors that influence learning and technology is one factor that is widely used to solve the limit by online tools like the calculator. These tools make the whole functionality just too easy to solve the limit but you also need to solve the limit manually.

The  calculator helps the students to learn the concepts of the limit. You can say the online tools are  just like the tutors for the students. They can learn and sharpen their concepts of difficult concepts of mathematics.

These concerts are just too difficult for the students to learn, but when you are online it makes the job easy for us. The proper use of the limit calc is to solve the limit by the tool but also try to solve the limit question manually. It helps to sharpen your concepts of mathematics. This is essential to know the whole working of the online tools and devices.

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