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In this section, we will investigate indeterminate forms and an new technique for calculating limits of such expressions.
Section 4.2 L’Hôpital’s Rule
Definition
A function having the property that as
it is true that ,
has an indeterminate form of type .
Definition
A function having the property that as
it is true that
has an indeterminate form of type .
For example:
Definition
A function having the property that as
it is true that ,
has an indeterminate form of type .
Definition
A function having the property that as
it is true that
has an indeterminate form of type .
For example:
Definition
A function having the property that as
it is true that ,
has an indeterminate form of type .
Definition
A function having the property that as
it is true that ,
has an indeterminate form of type .
For example:
TheoremL’Hôpital’s Rule
Let f and g be differentiable functions such that
has an indeterminate form of type or type .
Then:
Note the “a” above could be ±∞.
Example 1
Evaluate
Example 2
Evaluate
Example 3
Evaluate
Example 4
Evaluate
Example 5
Evaluate
Example 6
Evaluate
Example 7
Below is shown the graph of y = f(x). Find:
(a)
(b)
(c)
