What makes an expression indeterminate? Consider: We can hold one part of the expression constant: 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: We can hold one part of the expression constant: Once again, we have conflicting trends, so this form is indeterminate.

Finally, here is an expression that looks like it might be indeterminate : Consider: We can hold one part of the expression constant: The limit is zero any way you look at it, so the expression is not indeterminate.

Here is the standard list of indeterminate forms: There are other indeterminate forms using complex numbers, but those are beyond the scope of this class. 