The following curriculum information is taken from Indiana's official standards for Calculus, Advanced Placement.

The state of Indiana has established the following mathematics standards to make clear to teachers, students, and parents what knowledge, understanding, and skills students should acquire in Calculus, Advanced Placement:

1  Limits and Continuity

Students develop an understanding of the concept of limit by estimating limits from graphs and tables of values, and finding limits by substitution, and factoring rational functions. They extend the idea of a limit to one-sided limits and limits at infinity. They use limits to define and understand the concept of continuity, decide whether a function is continuous at a point, and find types of discontinuities. And they understand and apply two continuity theorems: the Intermediate Value Theorem and the Extreme Value Theorem.

Students understand the concept of limit, find limits of functions at points and at infinity, decide if a function is continuous, and use continuity theorems.

1.1  Understand the concept of limit and estimate limits from graphs and tables of values.

Example: Estimate ??? by calculating the function's values for $$x = 2.1, 2.01, 2.001 and for $$x = 1.9, 1.99, 1.999.

1.2  Find limits by substitution.

Example: Find ???

1.3  Find limits of sums, differences, producs, and quotients.

Example: Find ???

Example:

1.4  Find limits of rational functions that are undefined at a point.

Example: Find ???