The limits are sometimes not easy to solve, especially when we are dealing with complex rational limits. These kinds of limits are not solvable by the substitution method. In this case, the limit calculator can be the best tool to solve the limit. Students find it difficult, To what is meant by complex numbers and by irrational numbers. In this case, we need to solve the limit by the Least common denominator method, this is quite a difficult method to solve the limit.

There are certain conditions of using one of the methods of solving a limit.

## Do you know that!

The limit calculator can help us in defining which methodology is going to work here. For example, when the Limit calculator with steps shows, we are getting the defined polynomial by putting the limit value. Then we are going to use the substitution methodology. When we can find the roots of the function. Then we can use the factoring method. When we are not able to find the roots of the function, we are compelled to make the conjugate of the function. When the Limit calculator shows, we are dealing with the complex number, it means, we are going to apply the LCD or the Least common denominator methodology.

The limits of a function indicate that the function is finite. We can solve the various limits by using the 4 methods, the Substitution method, the factoring method, the rationalizing the numerator method, and the Least common multiple methods. When we solve the limits by any of the methods then the limits calculator with steps is one of the reliable methods to confirm, we are solving the limit exactly what is required.

We can also decide, which method is best to solve the limit by which methodology. It can be difficult for students to decide, which method to apply, as they are finding all the methods are applicable on the limits

In this article, we are discussing, when to choose a particular method:

## The reason for using the Substitution method?

The first technique, we are using the substitution method, we are using the substitution technique, when the function is not undefined by applying the limit.

For example consider the function:

F(x)=** ****x****5****x****2****-9x+18****x-4**

Reason for applying the substitution method:

- In the above function, the limit is upto “3”, we can apply the values of the limit to its extent, and the denominator is not becoming undefined by putting the values of the limit, which is “5”.
- We are going to use the other methods, if the limit is going “4”, in this case the denominator is becoming undefined and we are compelled to use the other methods to solve the limit. The limit calculator with steps also helps to define, where we are going to use which method.

F(x)=** ****x****4****x****2****-9x+18****x-4**

## When we are using the factoring method?

There are specific reason of using the factoring method, to solve the limit by using the factoring method, we are discussing them:

- The first thing, which is needed to satisfy the function, should be factorizable. The function which are having roots or the factors are not solved by the factoring method:

The function like:

F(x)=** ****x****4****x****2****-6x+8****x-4****, ** F(x)=** ****x****3****x****2****-9x+18****x-3****, ** F(x)=** ****x****2****x****2****-4x+4****x-2****,**

- You can observer the x 2-6x+8, x 2-9x+18, x 2-4x+4Consider all the functions that are factorizable like (x-4)(x-2), (x-6) (x-3),and (x-2)(x-2). These functions are factorizable, so we are applying the factoring method.
- When we are applying the limit in these functions, we are canceling the denominator. So we are applying the factoring methodology in solving these limits. We can use the limit solver in finding which methodology is best for solving a particular function of the limit.

## When we are using Rationalizing method?

The rationalizing methodology is used, when we have undefined denominators, and on the numerator side, there is no possibility of the factoring. The limit calculator with steps, can be best in solving the such an algebraic expression:

Now consider a polynomial,

F(x)=**x****11**x-5 -3x-11

- There is no possibility of making the factors of the numerator, and no possibility of substitution of the limit.
- When we put the limit in the numerator in this case, we are getting the undefined function, and we are getting the “0” in the denominator.
- So we are making the conjugate of the numerator, which is simple to make, we are just changing the symbol of the numerator and multiplying it both by the numerator and denominator.
- In this case the conjugate is x-5+3. We are multiplying it both the denominator and the numerator,
- x-5 -3x-11.x-5+3x-5+3, this is helping us to solve the limit without putting the value in the denominator, which is making the limit undefined. We can use the limit calculator with steps in solving the limit.

## When we are using the LCD method?

# We can use the limit calculator with steps, when we are dealing with the LCD method.

There are certain reason of using the LCD method:

- The most common is to use the LCD methodology especially when we are dealing with the complex rational number like

F(x)= x01 x+6x–16

- We need to take the LCD of the denominator to solve the limit, as on any point, when we are putting the limit, we are making it undefinable.

- We aren’t even able to make the conjugate of the function, so we are applying the LCD method, in solving the limit.

## The Last word:

The limit calculator with steps helps the students in defining which methodology we are going to apply. This helps the students, which method is applicable, to certain algebraic expressions. When we are able to define, which method is applicable to the algebraic expression with the help of the limit calculator. Then we can apply a certain methodology to the expression to solve the limit.

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