In this section, we will investigate indeterminate forms and an new technique for calculating limits of such expressions.

A function having the property that as it is true that, has an indeterminate form of type.

A function having the property that as it is true that has an indeterminate form of type. For example:

A function having the property that as it is true that, has an indeterminate form of type.

A function having the property that as it is true that has an indeterminate form of type. For example:

A function having the property that as it is true that, has an indeterminate form of type.

A function having the property that as it is true that, has an indeterminate form of type. For example:

Let f and g be differentiable functions such that has an indeterminate form of type or type. Then: Note the “a” above could be ±∞.

Evaluate

Below is shown the graph of y = f(x). Find: (a) (b) (c)