Indeterminate Forms and L

1
Indeterminate Forms and LHopitals Rule Part 2

• Chapter 4.4
• April 17, 2007

2
Indeterminate Forms

• Any limit of the form
  is called an indeterminate form of type .
• We call the form an
  indeterminate form of type .
• Other Indeterminate forms are

3
LHopitals Rule applies ONLY to indeterminate
forms
If the
Or
Provided the limit on the right exists (or is
or )
Then
Indeterminate form
Take for example
4
However we can manipulate expressions of other
forms so they fit the criteria
The form is
LHopitals does not apply, but if we rewrite the
limit as
the resulting form will be or And we can
apply LHopitals Rule.
5
However we can manipulate expressions of other
forms so they fit the criteria
The form is
LHopitals does not apply, but if we rewrite the
limit as a quotient (finding a common
denominator) the resulting form will be
or And we can apply LHopitals Rule.
6
Example
The form is
LHopitals does not apply, but we can combine the
log term using properties of logs Which gives
us the form
7
The last forms involve
exponents and well use these properties of
logsin our solution.
The form is
LHopitals does not apply, but if we rewrite the
function in terms of e using the first property
of logs
We can use the second property and find the limit
using our previous forms.
8
More Examples
9
Try
10
More Examples
Determine a value of b for which
Is finite.
b 0
Determine a value of b for which
Is finite.
b 8
Determine the behavior of the limits
Both diverge