4.7 / 10 Actionthri... Now

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

. 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 4.7 / 10 ActionThri...

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

∞∞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 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

, can have a determined limit for their ratio based on their slopes (derivatives) at that point. ✅ Result