Skip to content
Calculation Machine

Limit Calculator (Rational Function at a Point)

Numerically estimate the limit of a rational function.

Reviewed by the Calculation Machine team · How we check our maths

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.

The formula

lim x->p of f(x), evaluated numerically

Worked example

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

Result

  • Limit estimate3
  • Left approach value2.99999
  • Right approach value3.00001

How to use the Limit Calculator (Rational Function at a Point)

  1. 1Enter the numerator and denominator coefficients.
  2. 2Enter the x value the limit approaches.
  3. 3The tool evaluates the function just left and right of that point and compares them.

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