Continuity Checker Calculator
Work out continuity checker instantly with clear inputs, formula shown and shareable results.
About Continuity Checker Calculator
A function is continuous at a point when it is defined there, the limit exists, and the two agree. A rational function fails only where the denominator vanishes, and there the failure is removable if the numerator vanishes too.
Formula
Continuity
f is continuous at a ⇔ f(a) exists and lim(x→a) f(x) = f(a)
Worked example
With the default values below, Continuity Checker Calculator returns Continuity of Removable discontinuity — the factor cancels. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator coefficients
- 1, -4
- Denominator coefficients
- 1, -2, -8
- Check continuity at x =
- 4
Results
- Continuity
- Removable discontinuity — the factor cancels
- f(x) where defined
- 0.00000000
- Limit from the left
- 0.166667
- Limit from the right
- 0.166667
Step by step
- 1Values used
- 2Continuity
- 3Continuity= Removable discontinuity — the factor cancels
- 4f(x) where defined= 0.00000000
- 5Limit from the left= 0.166667
- 6Limit from the right= 0.166667
Assumptions and limits
- The result is derived only from the 3 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 8 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 (x − 4)/(x² − 2x − 8) at x = 4?
The denominator factors as (x − 4)(x + 2), so the factor cancels and the discontinuity is removable with limit 1/6.
What is a jump discontinuity?
One where both one-sided limits exist but differ, as in a piecewise definition or the step function.