L’Hôpital’s Rule Evaluator

Step-by-step classroom tool for limits of the forms 0/0 and ∞/∞. Apply one derivative step at a time and see when the limit becomes evaluable.

Preset examples

Numerator f(x)

Denominator g(x)

Target x →

Max derivative steps

Current expression

sin(x)

Numerator near target

—

Denominator near target

—

Detected form

—

Step-by-step solution

Teaching note: L’Hôpital’s rule applies directly only to quotient limits of the forms 0/0 or ∞/∞, under the usual differentiability conditions. Forms such as 0·∞, ∞−∞, 1^∞, 0⁰, and ∞⁰ must first be rewritten into an appropriate quotient form.

Supported expressions: numbers, x, +, −, *, /, ^, parentheses, sin, cos, tan, exp, log, sqrt. Powers should use a constant exponent, e.g. x^3 or (x+1)^2.