Limit At Infinity Calculator
Work out limit at infinity instantly with clear inputs, formula shown and shareable results.
About Limit At Infinity Calculator
For a rational function the behaviour at infinity depends only on the degrees. Lower numerator degree gives 0, equal degrees give the ratio of leading coefficients, and higher numerator degree diverges.
Formula
Rational limits at infinity
deg n < deg d → 0; deg n = deg d → leading ratio; deg n > deg d → diverges
Worked example
With the default values below, Limit At Infinity Calculator returns Limit of Finite limit 0.5. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator coefficients, highest power first
- 3, 2, -1
- Denominator coefficients
- 6, 0, 4
- Approachone of x → +∞, x → −∞
- x → +∞
Results
- Limit
- Finite limit 0.5
- Finite limit value (0 when divergent)
- 0.50000000
- Value at a very large x
- 0.50000003
- Degrees compared
- numerator degree 2 versus denominator degree 2
Step by step
- 1Values used
- 2Rational limits at infinity
- 3Limit= Finite limit 0.5
- 4Finite limit value (0 when divergent)= 0.50000000
- 5Value at a very large x= 0.50000003
- 6Degrees compared= numerator degree 2 versus denominator degree 2
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 (3x² + 2x − 1)/(6x² + 4) as x → ∞?
The degrees match, so the limit is 3/6 = 0.5.
Why do lower-order terms not matter?
Dividing through by the highest power sends every lower term to zero, leaving only the leading coefficients.