L Hopital Rule Calculator
Work out l hopital rule instantly with clear inputs, formula shown and shareable results.
About L Hopital Rule Calculator
L'Hôpital's rule replaces a 0/0 quotient by the quotient of derivatives, repeating until substitution works. It is valid because near the point both functions behave like their linear approximations.
Formula
L'Hôpital's rule
if f(a) = g(a) = 0 then lim f/g = lim f'/g', provided the latter exists
Worked example
With the default values below, L Hopital Rule Calculator returns Limit value of 2.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator coefficients, highest power first
- 1, 0, -1
- Denominator coefficients
- 1, -1
- Limit point x
- 1
Results
- Limit value
- 2.00000000
- Indeterminate form
- Yes, it started as 0/0
- Times differentiated
- 1
- Final quotient used
- 2x over 1
Step by step
- 1Values used
- 2L'Hôpital's rule
- 3Limit value= 2.00000000
- 4Indeterminate form= Yes, it started as 0/0
- 5Times differentiated= 1
- 6Final quotient used= 2x over 1
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
Find the limit of (x² − 1)/(x − 1) as x → 1.
It is 0/0, so differentiate to get 2x/1 = 2.
Can I apply it to any quotient?
No. It requires an indeterminate form such as 0/0 or ∞/∞; applying it otherwise gives wrong answers.