8.7: Identifying Indeterminate Forms

Brooklyn Bridge, New York City Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008

What makes an expression indeterminate?

lim1000x

x

Consider:

We can hold one part of the expression constant:

1000lim 0x 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:

0

0lim1000 1x

x

Consider:

We can hold one part of the expression constant:

0.1limxx

Once again, we have conflicting trends, so this form is indeterminate.

0.1lim 0xx

Finally, here is an expression that looks like it might be indeterminate :

0

lim .1 0x

x

Consider:

We can hold one part of the expression constant:

lim .1 0x

x

The limit is zero any way you look at it, so the expression is not indeterminate.

1000

0lim 0xx

Here is the standard list of indeterminate forms:

0

1 00 0

0

0

There are other indeterminate forms using complex numbers, but those are beyond the scope of this class.