in this section, we will investigate indeterminate forms and an new technique for calculating limits...
TRANSCRIPT
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)