How to use the Limit Calculator
Type in a value of this functionEnter the function from which you need to find the limit (for example one-sided or two-sided limit) and click «Submit» button.
Learn a step-by-step solutionAfter each calculation, you can study the detailed step-by-step solution of the given function.
Save the results of your calculationAfter finishing, you can copy the calculation result to the clipboard, or enter a new problem to solve.
What is Limits?
Calculus is known as one of the critical fields of study in Mathematics. It is the study of continuous change. The branch of Calculus emphasizes the concepts of Limits, Functions, Integrals, Infinite series, and Derivatives. Limits is one of the essential concepts of calculus. It helps in analyzing the value of a function or sequence approaches as the input or index approaches a particular point. In other words, it depicts how any function acts near a point and not at that given point. The theory of Limits lays a foundation for Calculus; it used to define Continuity, Integrals, and Derivatives.
Limits are stated for a function, any discrete sequence, and even real-valued function or complex functions. For a function f(x), the value the function takes as the variable approaches a specific number say n then x → n is known as the limit. Here the function has a finite limit:Lim x→n f(x) = L
Where, L= Lim x → x0 f(x) for point x0. For all ε > 0 we can find δ > 0 where absolute value of f(x) – L is less than E when absolute value of x - x0 < δ. In the case of a sequence of real numbers, like a1, a2, a3,…, an. The real number L is the limit of the sequence:Lim n→ ∞ an = L
The value of the function f(x) can be found from the left or the right of the point n. The expected value of the function for the points to the left of the given point n is the left-hand limit, also called the below limit, while the points to the right of the specified point n is known as the right-hand limit even called the above limit. The limit on the left is defined by limx → x- 0 f(x) and the limit on the right is denoted by limx → x + 0 f(x).
It is important to understand that the limit exists only when the values derived for the left-hand limit and the right-hand limit are equal. While calculating the limit for complex-figured functions, there are unlimited modes to approach a limit for a point. In such situations to find a distinct value of the limit, there is a need forstricter standards. For the limit of a rational function of the type p(x) / q(x), the important step is to simplify the rational function to the form 0/0 for a given point.
There are various ways for the computation of limits depending on the different nature and types of functions. There is a great application of the L- Hospital's rule, which involves differentiating the numerator and denominator of rational functions or indeterminable limits, till the limit takes the form 0/0 or ∞/∞.