Transcript 8.2 Day 2 Identifying Indeterminate Forms

8.2 Day 2: Identifying Indeterminate Forms
Photo by Vickie Kelly, 2008
Brooklyn Bridge, New York City
Greg Kelly, Hanford High School, Richland, Washington
What makes an expression indeterminate?
Consider:


We can hold one part of the expression constant:
x
lim

x  1000
1000
lim
0
x 
x
There are conflicting trends here. The actual limit
will depend on the rates at which the numerator and
denominator approach infinity, so we say that an
expression in this form is indeterminate.

Let’s look at another one:
Consider:
0
We can hold one part of the expression constant:
lim1000 x  1
x0
lim x0.1  
x 
lim x 0.1  0
x 
Once again, we have conflicting trends, so this form
is indeterminate.

Finally, here is an expression that looks like it might
be indeterminate :
Consider:
0
We can hold one part of the expression constant:
lim .1  0
x
x
lim  .1  0
x
x
lim x1000  0
x 0
The limit is zero any way you look at it, so the
expression is not indeterminate.

Here is the standard list of indeterminate forms:


0
0


1
 0
0
0
0
There are other indeterminate forms using complex
numbers, but those are beyond the scope of this class.
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