Limit Calculator (Rational Function at a Point)
Numerically estimate the limit of a rational function.
Enter your values
ⓘ Live results
Results
- Limit estimate
- 3
- Left approach value
- 2.99999
- Right approach value
- 3.00001
Quick answer
The limit is estimated by evaluating the function extremely close to the target x from the left and right and checking they agree.
lim x->p of f(x), evaluated numerically
How to use the Limit Calculator (Rational Function at a Point)
- 1Enter the numerator and denominator coefficients.
- 2Enter the x value the limit approaches.
- 3The tool evaluates the function just left and right of that point and compares them.
Worked example
Using the values the calculator loads with:
Inputs
- Numerator a (x^2 coeff)1
- Numerator b (x coeff)-1
- Numerator c (constant)-2
- Denominator d (x coeff)1
- Denominator e (constant)-2
- x approaches2
Results
- Limit estimate3
- Left approach value2.99999
- Right approach value3.00001
Frequently asked questions
What if the denominator is zero at p?
The function may have a removable discontinuity or diverge — check if the numerator is also zero there.
Is this exact?
It's a numerical estimate; for exact limits use algebraic simplification (factoring, L'Hopital's rule).
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.