Students sometimes find it too difficult to implement the methodology of the limit.  The remaining undecided, what to implement, there are four methods of solving the limit. The limits calculator can be a good way to decide which method to implement. When you are finding the roots of the limit, then you can implement the factoring method. The other thing, students are unable to find the difference between rational and complex numbers. When students are unable to find a method in their mind, which method to implement, then it becomes a daunting task for the students. The main reason, for the students, is that they are unaware of what method to implement.

Do you know that!

The limit calculator with steps, helps the students to determine, which kind of number they are dealing with if they can easily get the information about the number identity. Then they can deal with a particular situation, and what kind of number they are dealing with. If you are putting the limit and getting an undefined number in the denominator, it means you can’t implement the substitution method. The limits calculator helps us in finding which method to implement, whether it is a substitution, factoring, rationalizing, or the Least common multiple methods. There are different functions in the limit solver, which help us to find which method to implement. The main reason, is we are able to find which kind of number we are dealing with, and what would be their outcome.

We need to find the reason of implementing a certain method:

Why use the substitution?

In the following examples, we are discussing two examples, where we are going to use the substitution method.

The substitution method should be applied, when the limit remains solvable, when applying the limit, consider the function below:

            F(x)=  x8x2-9x+18x-7

We are going to use the substitution method, as the limit remains solvable, when we are applying the limit in the above function. 

Now consider a function, a function given below, 

                     F(x)=  x4x2-9x+5x-4

Here the function, would become unsolvable, when we are implementing the limit, which in this case is  x4, it would make the denominator, undefined, when we are putting the limit in the function, in the denominator,  would become ‘0’.  The Limits calculator, would help in this regard, as we are able to find whether the function is undefined or not, before implementing the limit. When we are dividing the numerator, with the function, it would make the whole function undefined. We are going to use another method in this situation.

Why use factorization ?

The  Limits calculator would be greatly helpful in deciding, are we implementing the factoring method or not? If we are getting the roots of the function in hand, then we are going to implement the factoring method, otherwise not.

There are certain reason of implementing he the factoring method, to follow the answer of the by the factoring method:

                   F(x)=  x4x2-6x+9x-3,    F(x)=  x3x2-12x+36x-6,    F(x)=  x2x2-8x+16x-4,

Now consider all the function, these functions are factorizable, 

                                 x2-6x+9= (x-3)(x-3)

                                 x2-12x+36= (x-6)(x-6)

                                 x2-8x+16 = (x-4)(x-4)

All the functions having the rationalized roots, and all the functions are cut by the denominator.  When we are applying the Limits calculator at the start, and finding terh functions that have the roots, then we are going to solve the limit by the factoring method.

Students do need to practice the factoring, as they find it difficult to get a particular symbol: 

                  There is a short key in this regard multiplication would rather become difficult                               (–-)=+

   (+-)=  –  

   (++)=  +      

When students are able to get the product of these symbols, then they are easily able to multiply the factors and would be able to get the final answer of the question.  Factoring is the  most common thing, you have to learn to solve the algebraic expressions.                 

Why use rationalizing ?

The rationalizing method is used, when the limit is unsolvable by the factoring method,  and also by the substitution method. 

Now consider the function:

                                     F(x)=x14x-7 -3x-14

Now is the function, it is unsolvable, when we are implementing the limit. The Limits calculator makes the limit easy for us, as we are seeing the denominator would become ‘0’. It would make the whole limit unsolvable.

We are going to make the conjugate of the x-7 -3x-11.x-7+3x-7+3, and multiplying both by the denominator and numerator. This would make the limit solvable for the students.

When you are multiplying with the conjugate of the function, it would make the question rather easy for the students.

Why use the LCD method?

The Limits calculator, helps us to spot the function having the complex rational number. 

                F(x)= x01 x+6x–16

The complex number can’t be solved, without the LCD, as we are not able to make the factors of the limit, as the dividing  numerator is making the whole limit unsolvable.

We have to take the Least Common Multiple or LCD, of the denominator, in this case it is 1/x+6. The Limits calculator can be the best tool in this regard, when solving the complex number.

The main difficulty, when solving the limit!

Students do find difficulty in solving the limit, when they are unaware which method to implement on the function on hand. Once they are able to find which method to implement on the limit, then the whole problem would become rather easy. The limits calculator can be best in solving the limit, and deciding, whether the limit is factorable or not. It also makes the question a little easy for the students. It is one of the most essential things to increase the understanding of the function you are dealing with, once you have the understanding of the function. Then you are easily able to implement the  Substitution, Factoring, Rationalizing or the LCD method.

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