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

The key feature for Section 4.7 is , which simplifies the calculation of limits for indeterminate quotients by using derivatives. 4.7 / 10 ActionThri...

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

. 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 limx→af(x)=0 and limx→ag(x)=0limit over x right arrow a

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

, 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 , 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