L'Hospital's Rule
The first type occurs when the limit of a function results in a limit of and is said to be a limit of indeterminate form .
INDETERMINATE FORM :
The second type occurs when the limit of a function results in a limit of and is said to be a limit of indeterminate form .
INDETERMINATE FORM :
Let f(x) and g(x) be two functions that are differentiable on an open interval with point s, except maybe at s, and the first derivative of g(x) is not zero. If the limit of as x approaches s is of indeterminate form or then L'Hospital's Rule can be applied.
L'Hospital's Rule states that the limit of the quotient of the two functions is equal to the limit of the quotients of their first derivatives.
L'HOSPITAL'S RULE:
If f(x) and g(x) are differentiable on an open interval that contains s (except maybe at s) and the limit is of indeterminate form or , that is:
AND
OR
AND
Then the following rule applies:
Let's look at some examples.
Step 1: Ensure that the limit is of indeterminate form or . |
Take the limit:
|
Step 2: Apply L'Hospital's Rule Because the limit is of indeterminate form , L'Hospital's rule can be applied.
|
Take the derivative Take the limit |
Step 1: Ensure that the limit is of indeterminate form or . |
Take the limit:
|
Step 2: Apply L'Hospital's Rule Because the limit is of indeterminate form , L'Hospital's rule can be applied.
|
Take the derivative Take the limit |
Related Links: Math algebra Circle: Center-Radius Equation Circle: General Equation Pre Calculus |
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