L'Hôpital's Rule Calculator
Apply L'Hôpital's rule numerically to evaluate 0/0 or ∞/∞ indeterminate limits.
About L'Hôpital's Rule Calculator
L'Hôpital's rule states that for 0/0 or ∞/∞ indeterminate forms: lim f(x)/g(x) = lim f'(x)/g'(x), provided the latter limit exists. This calculator applies the rule numerically by computing derivatives via central differences. It can apply the rule up to 5 times for persistent indeterminate forms.
Formula
L'Hôpital's rule
lim(x→a) f(x)/g(x) = lim(x→a) f'(x)/g'(x) when f(a)/g(a) is 0/0 or ∞/∞
- f(x)
- Numerator function
- g(x)
- Denominator function
- a
- Approach point
Worked example
With the default values below, L'Hôpital's Rule Calculator returns Limit of 1.0000000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator f(x)
- sin(x)
- Denominator g(x)
- x
- x approaches
- 0
- Max applicationsaccepts 1–10
- 5
Results
- Limit
- 1.0000000000
- Applications of L'Hôpital
- 1
- Indeterminate form
- 0/0
Step by step
- 1Values used
- 2L'Hôpital's rule
- 3Limit= 1.0000000000
- 4Applications of L'Hôpital= 1
- 5Indeterminate form= 0/0
Assumptions and limits
- The result is derived only from the 4 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
When can L'Hôpital's rule be applied?
Only when the limit gives an indeterminate form: 0/0 or ∞/∞. For other forms like 0·∞ or 1^∞, algebraic manipulation is needed first.
What if repeated application doesn't resolve it?
Some limits require algebraic simplification or other techniques. The calculator falls back to direct numerical evaluation near the point.