4.7 / 10 Actionthri... -

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

∞∞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

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 4.7 / 10 ActionThri...

limx→af(x)=±∞ and limx→ag(x)=±∞limit over x right arrow a of f of x equals plus or minus infinity and limit over x right arrow a of g of x equals plus or minus infinity

∞∞the fraction with numerator infinity and denominator infinity end-fraction Feature Overview: L'Hôpital's Rule The key feature for Section 4

4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms - Calculus. flippedmath.com Calculus I - L'Hospital's Rule and Indeterminate Forms

. 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 Do not use the Quotient Rule

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