One Sided Limit Calculator
Work out one sided limit instantly with clear inputs, formula shown and shareable results.
About One Sided Limit Calculator
One-sided limits approach a point from below or above. The ordinary two-sided limit exists only when both agree, which is why a removable discontinuity still has a limit but a jump does not.
Formula
Two-sided limit
lim exists ⇔ left limit = right limit
Worked example
With the default values below, One Sided Limit Calculator returns Limit from the chosen side of 4.999999. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator coefficients
- 1, -1, -6
- Denominator coefficients
- 1, -3
- Approach x =
- 3
- From which sideone of Both sides, From the left, From the right
- Both sides
Results
- Limit from the chosen side
- 4.999999
- Limit from the left
- 4.999999
- Limit from the right
- 5.000001
- Two-sided limit
- Yes, both sides agree so the limit exists
Step by step
- 1Values used
- 2Two-sided limit
- 3Limit from the chosen side= 4.999999
- 4Limit from the left= 4.999999
- 5Limit from the right= 5.000001
- 6Two-sided limit= Yes, both sides agree so the limit exists
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
For (x² − x − 6)/(x − 3) as x → 3?
The factor (x − 3) cancels leaving x + 2, so both one-sided limits are 5 and the limit exists.
When do the sides disagree?
At a jump, as with |x|/x at zero, which approaches −1 from the left and +1 from the right.