L'Hôpital's Rule Calculator
Apply L'Hôpital's rule numerically to evaluate 0/0 or ∞/∞ indeterminate limits.
Inputs
Numerator function.
Denominator function.
Limit
1.0000000000
Applications of L'Hôpital
1
Indeterminate form
0/0
Step by step
Values used
Numerator f(x) = sin(x); Denominator g(x) = x; x approaches = 0; Max applications = 5
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 ∞/∞
Limit
= 1.0000000000
Applications of L'Hôpital
= 1
Indeterminate form
= 0/0
How it works
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
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.