Limit Calculator | Process to calculate the Limit Function

Use this online Limit Calculator to know the limit of a function by replacing the variable value. Enter your function and variable value as the inputs in the below fields and get the result by tapping on the calculate button in a fraction of seconds.

Limit Calculator: Are you looking for easy ways to find function limits? Then, stop your search right here because we have come up with a simple method to compute the function limit in the given range. With the help of this handy Limit Calculator tool, you can easily calculate the limit and know the output automatically. Furthermore, you can also check the steps to solve the function limit with a best example and its form.

How to get the Limit of a function?

The limits are used to define the integrals, derivatives, and continuity. The limit function is a concept in the analysis which concerns the behavior of a function at the particular moment. Here we are offering the stp by step process to evaluate a limit function. Checkout the below sections and follow them while calculating a limit function in the given range.

  • Take a limit function and substitute the variable value to get the output this is called substitution.
  • If the above substitution method fails, then follow this factorization method. Especially, use this method when the function is a polynomial expression.
  • Do factorization of the given function, cancel the similar terms and substitute the variable value.
  • When a function is having the square root in the numerator and polynomial expression in the denominator, solve it by rationalizing the numerator.
  • Solve the expression and substitute the variable value in it.

Basic Form

The standard form to represent the limit function is lim x to c f(x) = L


C is a real number

f is a real valued function



Question1: Solve Lim x->5 x^2-6x+8 / x-4?



Here we use the substitution method

f(x)=x^2-6x+8 / x-4

f(5) = 5^2 – 6*5 + 8 / 5-4 = 25-30+8 / 1 = 3

Therefore, the solution is 3.

Question2: Solve lim x->4 x^2-6x+8 / x-4?



f(x)=x^2-6x+8 / x-4

Substitution process does n’t work here. Because the denominator can’t be zero.

Check out the factorization method

After factorization the f(x) can be as follows

f(x) = (x-4) * (x-2) / (x-4)

After cancelling f(x) = x-2

f(4) = 4-2 = 2

The answer is 2

Frequently Asked Questions on Limit

1. What is the limit formula?

lim x->a f(x) is the limit formula. This is called the limit of a function f(x) at an interval x=a.

2. What are the five laws of limits?

The list of limit laws are here.

  • Constant Law limx->a k=k.
  • Identity Law limx->a x=a.
  • Sum Law limx->a f(x)+g(x) = limx->af(x) + limx->ag(x)
  • Difference Law limx->a f(x)-g(x) = limx->af(x) – limx->ag(x)
  • Constant Coefficient Law limx->a k*f(x) = klimx->af(x)
  • Multiplication Law limx->a f(x)*g(x) = limx->af(x) * limx->ag(x)

3. What is the limit of a constant?

The limit of a constant function is always a constant.

4. What is the limit?

In maths, a limit is the value that a function approaches as the input and approaches some value.

5. Solve limx->13 square root (x-4)-3 / x-13 using the rationalizing the numerator process?

After rationalizing the numerator, we will get the expression as 1 / square root of x-4 +3. Substitute the value. the value is 1/16.

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