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# Teaching the concepts of limits in Math by using technology

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Technology has totally changed the concepts of learning difficult concepts of the Mathematics. Digital tools and apps like limit calculator by calculator-online.net, when you are using the tools.It also increases the understanding of different methods of the limits. It is best to clear the concepts of the students by letting them know, there are two types of limits. The infinite limit and finite limits. We are going to use the finite limits by substitution, and by factoring method. The infinite limits are going to be solved by the rationalizing and least common denominator(LCD) methodology. Students normally not able to recognize, whether the limit is finite or infinite.

There are different methods to implement technology to learn the concept of the limit, we use apps like limits calculator to find which methodology is best for the students.

## 1: Substitution method:

The substitution method is going to be used on the limits on the algebraic function, where the

f(x)x8x2-8x+18x-7

You can observe, when we apply limit, then denominators  f(x)x8(8)2-8(8)+188-7 and we are getting the answer of the limit, the lim calculator by calculator-online.net helps us, whether the question is solvable by the substitution method or not.

## 2: Factoring method:

For solving the limit by the factorization method, you need the roots of the limit, and the limit solver isassiting whether the quadratic function has the real roots or not. Now let consider an example:

f(x)x12x2-12x+12x-12

It should be realized, the numerator (x2-12x+36) in the function above the function has real roots. In this case the roots of the (x-12)(x-1). The numerator is canceled by the denominator and, then we can apply the limit

f(x)x12x2-12x+12x-12= x12(x-12)(x-1)x-12=(x-1)=12-1=11

When you are using technology and apps like limit calculator by calculator-online.net, then it can be easy to solve the limit.

### The rationalizing method:

The rationalizing method is going to be used when we dealing with the algebraic functions having the square roots like:

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

We are going to the conjugate x-7 -3x-14.x-7 +3x-7 +3, and making the limit insolvable form, the limit calculator is going to recognize which method is the best to solve the limit.

### The LCD method:

The complex numbers limit is only going to be solved by the LCD method, and

f(x)= x01 x+7x17

For such numbers it is best to use the LCD method, as it makes the algebraic function a solvable limit and we can simply apply the limit to the  function.

There are different methods to implement technology to learn the concept of the limit, we use apps like limits calculator to find which methodology is best for the students. It is essential for the students to recognize which method is best suited to solve a limit. 