Limit calculator
With this limit calculator you find the limit of a function at a point or at infinity: enter the function and the point, and you get the result along with a table of values from the left and right.
Source: Wikipedia – Grenzwert (Funktion): links-/rechtsseitiger Grenzwert, uneigentliche Grenzwerte. Updated: .
How it is calculated
The limit limx→a f(x) is the value f(x) approaches as x gets closer and closer to a. For sin(x)/x at 0 it is 1, even though the function is not defined there.
How it is calculated
The calculator approaches the point from the left and the right with ever smaller distances (halved each time), or runs outward for ±∞. From the function values it picks the range with the least scatter, so it is neither too coarse nor distorted by rounding errors. If the magnitude keeps growing it reports ±∞; if left and right differ, there is no limit.
Good to know
- A limit exists only if the left- and right-hand limits agree – for 1/x at 0 they do not.
- The result is a calculation, not a proof. For exams you still need the working (cancelling, L’Hôpital, squeeze theorem).
- If the calculator recognises a familiar value such as e, π or a simple fraction, it adds it as a suggestion.
Frequently asked questions
How do you calculate a limit?
Plug in values that get closer and closer to the point, or transform the expression (cancel, L’Hôpital). This calculator does the numerical approach from both sides.
When does a limit not exist?
When the left- and right-hand limits differ (e.g. |x|/x at 0), when the function runs off to infinity, or when it keeps oscillating (sin(1/x) at 0).
How do I enter infinity?
Enter inf or ∞ as the point for +∞ and -inf for −∞. The calculator then checks the behaviour for very large or very small x.
What is the difference between a limit and a function value?
The function value is f(a) itself; the limit is the behaviour near a. For a gap such as (x²−1)/(x−1) at 1 there is no function value, but the limit is 2.
Sources and legal basis
- Wikipedia – Grenzwert (Funktion): links-/rechtsseitiger Grenzwert, uneigentliche Grenzwerte
- Wikipedia – Aitken's delta-squared process (Extrapolation geometrisch konvergierender Folgen)
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