In the preceding Chapter, each time we needed to find a function’s derivative we started with the Definition of the Derivative, $f'(x) = \lim_{h \to 0}\dfrac{f(x+h) – f(x)}{h},$ and proceeded from there. You probably found this process cumbersome and time-consuming, as does everyone. Since we will be computing many derivatives as we proceed, we need… [read more]

If you can, start your study of Calculus with this Chapter: we immediately begin using introductory ideas in Calculus so you can get a sense for what Calculus is about before you dive more deeply into developing the key tools. On the very first screen you’ll be doing Calculus calculations, based on the reasoning-skills you… [read more]

Here we develop the foundational concept of the limit, without which the entire field of Calculus would not exist. We’ll introduce the formal definition of the limit, and then learn how to calculate limits for a wide variety of functions. We end the Chapter by defining continuity, a definition that relies on limits; understanding a… [read more]