Evaluate polynomial ratio limits using direct substitution and L'Hôpital's rule for indeterminate forms.
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Numerator terms
Denominator terms
Result
Step-by-step
Also in Calculus
Calculus
A limit calculator evaluates the limit of a rational function (polynomial divided by polynomial) as x approaches a given value. It uses direct substitution first, then applies L'Hôpital's rule for indeterminate forms like 0/0.
Start with direct substitution — plug the approach value into the function. If the result is a defined number, that is the limit.
If substitution yields 0/0 (indeterminate form), apply L'Hôpital's rule: take the derivative of the numerator and denominator separately, then re-evaluate the limit.
Frequently asked questions
An indeterminate form like 0/0 or ∞/∞ means the limit cannot be determined by direct substitution alone. Additional techniques like L'Hôpital's rule or algebraic manipulation are needed.
When the numerator is nonzero and the denominator approaches zero, the limit is ±∞ (or does not exist), depending on the sign of the expressions near the approach value.
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