How You Calculate Limits in Math by Using Technology

Updated on November 26, 2021 | by Evan Chase

The limits of a calculator are used to define the function as finite in nature, as the finite function has limits and boundaries. The infinite function has no boundaries or limits as they are limitless or infinite in nature. Now we are also using technology like limit calculator as this is a powerful device to solve the problem. These days there are more and more powerful devices and technologies that have the ability to solve the limits of the functions by the use of the limit solver online devices. 

These devices are useful for a number of reasons, as we can find the answer of various limits by the use of these devices as their answer was quite difficult to find algebraically. You can also check the answer to the solved limits by these devices, as we have solved on the paper. When we are using limits algebraically, we need to make a table to confirm our answer. This table is made to find the behavior of the number near the arrow number. 

We made the table to get a numerical grasp on the problem at hand and it also helped to increase the algebraic understanding of the question.  When you make the graph of the function, you can double-check the answer of the limit, which you have found by using the limits calculator, so you have a much more enhanced spectrum when you are using these devices to solve the limit questions.

In this article, we are discussing how we can solve a limit question by using a limit calculator with steps

The Method of Solving Limits by Calculators:

We can solve most of the limit questions by using the limit calculator. We use two basic methods to solve the limits by using the calculators:

Now see a limit which we need to solve by the calculator:

x→5×2-25x-5, we want to solve this question by using a limit calculator with steps

Method One of solving the limit:

Now we just take a number extremely close to the number 5 and enter the value into the “x”, then we need to follow the steps given below:

  • Step 1: Enter the number, for example, 4.9999 on the home screen, and then press the Sto (store) key, then the “x” button, and then the Enter button. When you do this procedure, you would store the number into the “x”. 
  • Step 2:  Now Enter the function:

                    y=   x2-25x-5

  • Step 3: Now hit the Enter button, the result would be 9.9999, which is extremely close to a round number or a figure, which is 10. Which is your answer to the limit.
  • Step 4:  For accurate measurement store the 4.999999 into the x, and follow the procedure given in Step 2.

Scroll the function back and hit the Enter button, The result would be rounded to the values of “10”, the number 9.999999 is not “10”, but the limit calculator representing in the rounded form which is “10” and this is your answer.

Method Two of Solving the Limit:

The second method of solving a limit is to produce a table of values, and to solve the question by using the limit calculator:

  • Step 1: Now in the graphing mode of the calculator, we need to enter the following function:

 So, by entering the function:

                            x2-25x-5

  • Step 2:  Now Go to the “Table set up” and enter your limit which is “5” and the table starts the number.
  • Step 3: Now Enter a small number like 0.001 for the “∆T”, this is the incremental value to the limit or the x-incremental in the table.
  • Step 4: Now hit the table button to produce the table of the limit. We are solving it by using the limit calculator. Scroll up so you can see a couple of numbers< 5, or less than the number “5”. You would observe a table of values like it is the following table:

       Table for  x2-25x-5after scrolling up to 4.998


              X                                 Y

           4.998                                9.998

           4.999                                9.999

           5                                       Error

           5.001                               10.001

           5.002                               10.002

           5.003                               10.003

Now you get the values of the “Y” close to we add any digit in the values of the “X”, so we find the limit of the function is around “10” which is our answer to the question by using the limit calculator, which is our required answer to the limit of the solved algebraic function.

Usefulness by Using the Calculator:

There is a number of reasons, why the calculator is useful, when solving the limits of the algebraic functions, we are presenting some of them here:

  • You can find the answer to the function, which is impossible to get algebraically, as you would not be able to solve the fractions for each value.
  • You need a lot of time to solve these difficult fractions on paper, it may take hours to solve, but by the limit calculator, it has been solved in steps and you can understand each step thoroughly.
  • The step-by-step solution of the limit gives you enough information about each step.
  • The questions, you are able to solve on the paper by using your copy and pencil, you can check by using your limit calculator

Many problems can be solved by two to three methods in Mathematics. We can use algebraically, graphically, and also numerically these questions. When we are using two to three approaches we can cross-check the answer of the question, whether we solved it correctly when the answer is the same, we can cross-check the question. The other thing, which is really important for your knowledge, is that each technique provides you with a really new approach and grasp of new concepts.

This increases your grip on various types of concepts of Mathematics. Like in the above question, we used the limit calculator to solve the question by two to three methods, the two methods we used by the calculators, and one is done on the paper manually, this has given us enough information about the question to cross-check the answer. 

 

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