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. If the result is still indeterminate, you can apply the rule again. Example Visualization The following graph illustrates how two functions, , both approaching zero at a point

: First, evaluate the limit directly. If it yields 000 over 0 end-fraction 4.7 / 10 ActionThri...

, can have a determined limit for their ratio based on their slopes (derivatives) at that point. ✅ Result If it yields 000 over 0 end-fraction ,

∞∞the fraction with numerator infinity and denominator infinity end-fraction Feature Overview: L'Hôpital's Rule - Calculus

L'Hôpital's Rule allows you to resolve indeterminate limits by differentiating the numerator and the denominator separately. Suppose that are differentiable and on an open interval that contains (except possibly at

limx→af(x)g(x)=limx→af′(x)g′(x)limit over x right arrow a of f of x over g of x end-fraction equals limit over x right arrow a of f prime of x over g prime of x end-fraction provided the limit on the right exists (or is ±∞plus or minus infinity Step-by-Step Application

4.7 Using L'Hopital's Rule for Determining Limits of ... - Calculus