4.7 / 10 Actionthri... May 2026

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

∞∞the fraction with numerator infinity and denominator infinity end-fraction , the rule can be applied. : Take the derivative of the top function ( ) and the derivative of the bottom function ( ) independently. Do not use the Quotient Rule . Re-evaluate the Limit : Find the limit of the new fraction f′(x)g′(x)f prime of x over g prime of x end-fraction 4.7 / 10 ActionThri...

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 Re-evaluate the Limit : Find the limit of

limx→af(x)=0 and limx→ag(x)=0limit over x right arrow a of f of x equals 0 and limit over x right arrow a of g of x equals 0 4.7 / 10 ActionThri...

The key feature for Section 4.7 is , which simplifies the calculation of limits for indeterminate quotients by using derivatives.