Many students incorrectly evaluate the indeterminate forms of type 00 , type (infinity)0 , and type 1(infinity) as 1 because they think that "anything to the zero power is 1" and "1 to any power is 1

Many students incorrectly evaluate the indeterminate forms of type 00 , type (infinity)0 , and type 1(infinity) as 1 because they think that "anything to the zero power is 1" and "1 to any power is 1." These rules are indeed true for powers of numbers. But 00 , (infinity)0 , and 1(infinity) are not powers of numbers but descriptions of limits. In this lab, we will see that these indeterminate forms can produce limits that are nonnegative real numbers or limits that are infinite.

1. We will need to use the following result from Chapter 2: if lim ( )... Find the theorem that justifies this result.

2. An indeterminate form of the type 00 can be any positive real number. Let a be a positive real number. Show that (ln )/(1 ln )