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 …

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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| < …

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