Limit Calculator
Evaluate the limit of f(x) as x approaches a value by numerical approximation from both sides.
About Limit Calculator
Evaluates lim(x→a) f(x) numerically by computing f(a±h) for progressively smaller h values and checking if the left and right limits converge to the same value. If they agree within tolerance, the two-sided limit exists. Otherwise, the one-sided limits are reported separately.
Formula
Numerical limit
lim(x→a) f(x) ≈ f(a ± h) as h → 0
- a
- Approach point
- h
- Decreasing step sizes from 1e-2 to 1e-8
Worked example
With the default values below, Limit Calculator returns Limit of 1.0000000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- sin(x)/x
- x approaches
- 0
Results
- Limit
- 1.0000000000
- Left limit (x→a⁻)
- 1.0000000000
- Right limit (x→a⁺)
- 1.0000000000
- Status
- Two-sided limit exists
Step by step
- 1Values used
- 2Numerical limit
- 3Limit= 1.0000000000
- 4Left limit (x→a⁻)= 1.0000000000
- 5Right limit (x→a⁺)= 1.0000000000
- 6Status= Two-sided limit exists
Assumptions and limits
- The result is derived only from the 2 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 10 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
What if the limit does not exist?
If the left and right limits differ, the two-sided limit does not exist. Both one-sided values are reported so you can see the discontinuity.
Can I find limits at infinity?
Enter a large value like 1000000 for x approaches. The calculator evaluates from both sides of that point.