Limit Calculator (Rational Function at a Point)
Numerically estimate the limit of a rational function.
Enter your values
Enter the numerator a (x^2 coeff) you are working with.
Enter the numerator b (x coeff) you are working with.
Enter the numerator c (constant) you are working with.
Enter the denominator d (x coeff) you are working with.
Enter the denominator e (constant) you are working with.
Enter the x approaches you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Numerically estimate the limit of a rational function. |
|---|---|
| Category | Math |
| Inputs needed | Numerator a (x^2 coeff), Numerator b (x coeff), Numerator c (constant), Denominator d (x coeff), Denominator e (constant), x approaches |
| Main output | Limit estimate |
| Formula | lim x->p of f(x), evaluated numerically |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Numerator a (x^2 coeff)
- Enter the numerator a (x^2 coeff) you are working with.
- Numerator b (x coeff)
- Enter the numerator b (x coeff) you are working with.
- Numerator c (constant)
- Enter the numerator c (constant) you are working with.
- Denominator d (x coeff)
- Enter the denominator d (x coeff) you are working with.
- Denominator e (constant)
- Enter the denominator e (constant) you are working with.
- x approaches
- Enter the x approaches you are working with.
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).
What do I need to enter into the Limit Calculator (Rational Function at a Point)?
Just 6 values: numerator a (x^2 coeff), numerator b (x coeff), numerator c (constant), denominator d (x coeff), denominator e (constant), x approaches. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Limit Calculator (Rational Function at a Point) work out the answer?
The limit is estimated by evaluating the function extremely close to the target x from the left and right and checking they agree. It applies the formula lim x->p of f(x), evaluated numerically and shows the working so you can check each step by hand.
Is the Limit Calculator (Rational Function at a Point) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.