This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.

In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and logarithmic functions.

This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.

The definite integral generalizes the concept of the area under a curve. We lift the requirements that ... be continuous and nonnegative, and define the...

Throughout our study of calculus, we will encounter many powerful theorems concerning such functions. The first of these theorems is the Intermediate Value Theorem.

For the following exercises, solve using calculus, then check your answer with geometry. 56. Determine the equations for the sides of the square that touches the unit circle on all four …

Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using our accompanying online resources.

We start by asking how to calculate the slope of a line tangent to a parametric curve at a point. Consider the plane curve defined by the parametric equ...

The first two limit laws were stated in Two Important Limits and we repeat them here. These basic results, together with the other limit laws, allow us ...

Let’s first take a closer look at how the function ... behaves around ... in Figure 2.12. As the values of x approach 2 from either side of 2, the value...