Limit Calculator

Do you want to find the limit values functions? Look no further as our limit calculator is here to help you find the limit values functions that give output.

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Introduction to Limit Calculator with Steps:

Limit calculator is an online limit measuring tool that helps you to find the solution of the limit values function that gives the output as it goes to the value of x.

Limit Calculator with Steps

Our limits calculator also helps to evaluate the limit value in the graph to check whether the function is continuous or not on a given interval in a couple of minutes.

What is a Limit?

Limits are the fundamental concept of calculus that helps to understand the behavior of a function approaching a certain point. Limit is defined as the real number function f in calculus that gives the closest values of x variable.

Limit calculations can be challenging if an indeterminate form exists, i.e. 0/0 or ∞/∞. Here we use L Hopital's rules process to solve it. If you are caught up in indeterminate forms, consider using our l hopital rule calculator to easily find the limit. In calculus, limit method is used for integrals, derivatives, or continuity of functions.

Rules Followed by Our Limits Calculator:

Now you would be wondering how to find the limit. For limit problems, different rules are used to solve various types of limit problems in calculus. These rules give the nearest values that approach x variables. The rules upon which the limit calculator with steps works are,

1. Sum Rule:

When two limit functions of one variable are found in the form of a sum then using the sum rule limit gets separated so that it can easily find the limit function.

$$ \lim_{x \to c} \biggr(f(x) + g(x) \biggr) \;=\; \lim_{x \to c} f(x) + \lim_{x \to c} g(x) \;=\; L + M $$

2. Difference Rule:

If the limit is the difference between two functions then the lim calculator separates it into two limit functions and the difference sign remains the same.

$$ \lim_{x \to c} \biggr(f(x) - g(x) \biggr) \;=\; \lim_{x \to c} f(x) - \lim_{x \to c} g(x) \;=\; L - M $$

3. Product Rule:

The limit of a product of two functions is the change into two limit product functions and then the limit calculator with steps applies the limit so that the limit exists.

$$ \lim_{x \to c} \biggr(f(x) * g(x) \biggr) \;=\; \lim_{x \to c} f(x) * \lim_{x \to c} g(x) \;=\; L * M $$

4. Constant Multiple Rule:

If the given function has a constant then the limits calculator keeps the constant separate from the limit function and the limit is applied only to the variable function not to the constant.

$$ \lim_{x \to c} \biggr(k * f(x) \biggr) \;=\; k \lim_{x \to c} f(x) \;=\; k * L $$

5. Quotient Rule:

If a quotient of two functions has a limit then the limit calculator divides the limit into the denominator or numerator separately but the limit of the denominator is not zero

$$ \lim_{x \to c} \biggr(\frac{f(x)}{g(x)} \biggr) \;=\; \frac{\lim_{x \to c}f(x)}{\lim_{x \to c}g(x)} \;=\; \frac{L}{M}, M ≠ 0 $$

These are the rules of limit, if you do the calculation of the limit problem by using the lim infinity calculator it applies these rules manually and it saves a lot of time.

Our limit solver with steps just takes your function and give you a precise solution immediately because it has built-in limit rules in its server.

Evaluation Procedure of the Lim Calculator:

The limit graphing calculator uses the above mentioned limit rules to solve various types of limit problems as limits share their role in calculus, continuity of a function, derivative, integral, and indeterminate functions.

You need to enter the limit problem in the tool and it will identify the behavior of your given function. As per your limit problems, our limit solver with steps analyze the input to know which method should be applied. These methods are given below.

Limit Evaluation through Algebraic Formulas:

This method includes limit evaluation through algebraic formulas like (a+b)² = a² + b² + 2ab, (a² - b²) = (a+b) (a-b) etc.

If your given limit function gives zero or undefine value after applying the limit, consider calculating the definition of derivative before using the lim infinity calculator as it uses algebraic formula to solve limit function.

After solving the limit function in the simplest form. The limits calculator again applies the limit so that you get the solution in numbers.

Limit Evaluation through the Factorization Method:

The lim calculator solves the limit problems with the factorization method to change the given function into the smallest form. After that, it applies limits and give the easiest solution.

Differential Method for Indeterminate Limits:

If a given limit function always gives an undefined answer despite applying different methods, then our lim to infinity calculator uses the differential method. This method is helpful in converting the indeterminate form of the limit into the determinate form easily.

Above all these methods, our limit calculator uses other of methods as well. It depends on the limit problem. To understand it, You need to know how to apply limits and for that you have to calculate the derivative of function first. Let's see an example to clarify it.

How to Find the Limit - Example:

An example of a limit function with a solution is given below to understand the manual calculation of solving such problems,

Example:

Calculate the limit of the following:

$$ \lim_{x \to 1} \frac{x^4 + x^2 - 1 }{x^2 + 5} $$

Solution:

$$ \lim_{x \to 1} \frac{x^4 + x^2 - 1}{x^2 + 5} \;=\; \frac{\lim_{x \to 1}(x^4 + x^2 - 1)}{\lim_{x \to 1}(x^2 + 5)} $$

$$ \frac{\lim_{x \to 1}(x^4) + \lim_{x \to 1}(x^2) - \lim_{x \to 1}(1)}{\lim_{x \to 1}(x^2) + \lim_{x \to 1}(5)} $$

$$ \frac{1^4 + 1^2 - 1}{1^2 + 5} \;=\; \frac{1}{6} $$

Steps of Using the Limit Calculator:

The limits calculator has a user-friendly interface that enables you to easily calculate the limit functions of x variable from the given limit function immediately.

You should follow some simple steps before using the limit graphing calculator for limit calculation. These steps are:

Enter your limit function in the input field.
Enter the limit value in its relevant number.
Select the one-side (minus, plus) or double-side limit function.
Click on the “Calculate” button to get the solution of the given limit function
Click on the “Recalculate” button to bring you back to a new page for more practice of limiting questions of xvariables.
If you want to try our lim calculator first to solve different types of limit variable functions to check the accuracy of its solution.

Outcome from Limit Solver with Steps:

The limit calculator provides you with the result of your given algebraic limit value problem in less than a minute after you press the calculated button. It may include the following:

Result option provides you the solution for the limit function of x variables.
Possible steps option provides you with solutions for algebraic functions in a complete step-wise process.
Plot option provides you with a solution in the form of a graph that shows you the limit values that are nearest to the x variable in a graph.

Benefits of Using Our Limit Graphing Calculator:

The limit solver provides you with a ton of benefits during the evaluation of limit function solutions that are present with different types of conditions in limits. These benefits are:

The lim infinity calculator provides you with a solution to an indeterminate form of function.
Our lim to infinity calculator saves time during finding the limit of a variable you just need to give input and it works automatically.
It is a trustworthy calculator that provides you solutions for limited one-variable limit problems with no mankind error.
The limits calculator is an educational tool that helps you to understand the concept of limit variable equations in mathematical operations.
This tool helps students to make assignments, projects, and reports because it provides accurate solutions whenever you use it for the limit calculation.
Our lim calculator allows you to access it from anywhere in the world, through an internet connection.
It is a free tool so you do not need to pay a single fee for the evaluation of limit problems.
The limit calculator with steps is a versatile tool that can handle various types of limit questions.

Related References

The definition of the limit
Definition and examples of limit
How to evaluate limit in calculus?
What is the formula of limit and how to calculate it?

Frequently Ask Questions

How to graph limits in calculus?

Graph limit in calculus involves imagining how the function acts as input comes to a particular value. The following steps can help you to understand graph limits:

Step 1: Firstly, you need to understand the basic concept of limits. Typically the limit approaches input to a specific point. Limits can be the left-hand limit and Right-hand limit, the right-hand limit approaches a point from the left. At the same time, the right-hand limit approaches a point from the right.

Step 2: Now you can start by plotting the graph of the function. It can be a rotational function, polynomial, trigonometric function or etc.

Step 3: Suppose you are computing the limit, so select the value of x. Basically it is a number where you suspect the function which has some special behavior like infinity and undefined point.

Step 4: You can analyze the behavior around the point with the help of three limits which are:

Finite limit: The limit is finite if the function’s approach to specific point from both sides.
Infinite limit: The limit is finite when the function is positive or negative approaches to point.
Limits that do not exist: When right-hand limits and left-hand limits are different or the function behaves untidily. So the limit does not exist.

Step 5: Draw the graph of the function which shows the limit value.

What is a one sided limit?

One sided limit is defined as a value function that approaches input (x) as a specific point from one side only. One sided limit is divided into two types which are discussed below,

Left hand limit:

It is denoted as lim x→a- f(x). It is the value that approaches x, as the function approaches c from the left side.

Right side limit:

It is denoted as lim x→a + f(x) is the value that approaches x, as the function approaches c from the right side.

How do you know if a limit is infinite?

The limit is infinite because the function value becomes larger, maybe it is positive or negative as the input approaches a certain point. It also depends on the function’s behavior to a specific value. There are two main conditions where a limit can be infinite.

X approaches to finite value (x = c)
X approaches positive infinity (X→∞)and negative infinity (X→- ∞).

How to know if a limit does not exist?

A limit does not exist if the function does not approach a single well-defined value as x approaches a specific point. Here are some points which describe why a limit does not exist:

When the left-hand limit and right-hand limit are different from each other.
The function oscillates without approaching a single value.
The function is undefined.

What is the limit chain rule?

The limit chain rule is defined as a method that helps you find the limit of complex functions by breaking them down into simpler components. The limit chain rule is only applied when the limit of the inner function exists and the outer function is continuous from the inner function.

Let’s find an example of a limit chain rule that clarifies the concept.

Example: Let's solve the limit of the function f(x) = √(x² + 1) as x approaches 1.

$$ Inner\; function:\; g(x) \;=\; x^2 + 1 $$

$$ \lim_{x \to 1} g(x) \;=\; 2 $$

$$ Outer\; function:\; h(u) \;=\; \sqrt{u} $$

$$ \lim_{u \to 2} h(u) \;=\; \sqrt{2} $$

Amanda Jepson

Last Updated February 21, 2024