Find Limit Calculator
Find limit calculator works out Limit and Limit as a number from Expression f(x), Variable and Approaching. The default figures on this page give limit of 1; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- f(x) = sin(x) / x
- Round 1: the quotient is in 0/0 form, so by L'Hôpital's rule differentiate top and bottom separately: cos(x).
- Substituting x = 0 now gives 1.
- Numeric check: at x = -1e-7 the value is 0.9999999999999983, which agrees.
Its 6 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the find limit calculator calculates
Evaluates the limit of an expression as the variable approaches a point or infinity, using direct substitution, L'Hôpital's rule for indeterminate quotients and degree comparison for rational functions, with every answer confirmed against a numeric sequence.
How to use this find limit calculator
Enter Expression f(x), Variable, Approaching and From which side. Limit updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Limit, Limit as a number and Notation.
The method follows OpenStax, Calculus Volume 1, chapter 2 (Limits) and section 4.8 (L'Hôpital's Rule) and OpenStax, Calculus Volume 1, section 4.6: Limits at infinity and the end behaviour of a rational function.
Removable singularity: (x^2 - 4)/(x - 2) as x → 2 example
With Expression f(x): (x^2-4)/(x-2), Variable: x, Approaching: 2, From which side: both, the calculator returns Limit as a number: 4, The limit exists: yes, Indeterminate form met: 0/0. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Limit, Limit as a number and Notation. The inputs you can vary are Expression f(x), Variable, Approaching and From which side.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What is the formula to find the limit?
On the figures this page opens with, the limit is 1. No single number fits everyone: it follows Expression f(x), Variable and Approaching, so enter your own above and the answer updates as you type.
How to find limit with calculator?
Evaluates the limit of an expression as the variable approaches a point or infinity, using direct substitution, L'Hôpital's rule for indeterminate quotients and degree comparison for rational functions. Open “How this is worked out” beside the result to see each step for your own figures.
How to calculate a limit?
It needs Expression f(x), Variable, Approaching and From which side. Nothing else is required, and the figures stay in your browser.
What is the formula for limits?
The result gives Limit, Limit as a number, Notation, The limit exists, Limit from the left and Limit from the right, each labelled with its unit so the figure can be read on its own.
What information do I need for the find limit calculator?
You need Expression f(x), Variable, Approaching and From which side. The page opens with default figures that give limit of 1, so you can see the scale before entering your own.
What does this find limit calculator show?
It shows Limit, Limit as a number, Notation, The limit exists, Limit from the left, Limit from the right, Indeterminate form met and How it was found, with the working and any warnings for your entries.