: First, evaluate the limit directly. If it yields 000 over 0 end-fraction
The key feature for Section 4.7 is , which simplifies the calculation of limits for indeterminate quotients by using derivatives. 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 : First, evaluate the limit directly
. 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 Suppose that are differentiable and on an open
∞∞the fraction with numerator infinity and denominator infinity end-fraction Feature Overview: L'Hôpital's Rule
∞∞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