# calculus

## Definition of a Derivative

I copy the definitions of three different types of derivatives from [1]: $\lim_{\Delta x \rightarrow 0} \frac{f(a+\Delta x) – f(a)}{\Delta x} \equiv \frac{d f(x)}{dx}\big|_{a}$ $\lim_{\Delta x \rightarrow 0^+} \frac{f(a+\Delta x) – f(a)}{\Delta x} \equiv \frac{d f(x)}{dx}\big|_{a^+}$ $\lim_{\Delta x \rightarrow 0^-} \frac{f(a+\Delta x) – f(a)}{\Delta x} \equiv \frac{d f(x)}{dx}\big|_{a^-}$ These definitions are best …

## Definition of a Limit

Math & physics largely depends on Calculus, so I copy a definition of a limit from [1]. A function $f(x)$ approaches a limit $A$ as $x$ approaches $a$ if, and only if, for each positive number $\epsilon$ there is another, $\delta$, such that whenever \$ 0 < |x-a| < …