L'Hopital's Rule Calculator

Evaluate indeterminate limits of the form 0/0 or ∞/∞ using derivatives.

Limit Settings

Numerator f(x)

Denominator g(x)

Limit point x → c

Check

f(0) ≈0.000000

g(0) ≈0.000000

Limit Evaluation

1.000000

Limit Value

Condition Met?Yes (0/0 or ∞/∞)

Numeric Result1.000000

Differentiation Step

\frac{f'(0)}{g'(0)} \approx \frac{1.0000}{1.0000} = 1.000000

What is L'Hopital's Rule?

L'Hopital's Rule provides a technique to evaluate limits of indeterminate forms (like 0/0 or ∞/∞). It states that the limit of the ratio of two functions is equal to the limit of the ratio of their derivatives.

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Pro Tips

Check Validity: Ensure the limit is actually 0/0 or ∞/∞ before applying the rule.
Differentiation: You differentiate the numerator and denominator separately, NOT using the Quotient Rule.
Repeated Use: If the new limit is still indeterminate, you can apply the rule again.

Fun Facts

"The rule is named after Guillaume de l'Hôpital, but it was actually discovered by his tutor, Johann Bernoulli."
"L'Hôpital published the rule in the first textbook on differential calculus in 1696."

Formula: \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}

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