Angle Addition Identities

This post includes proofs of two angle addition identities. $ \sin(x+y) = \sin x \cos y + \sin y \cos x$ $ \cos(x+y) = \cos x \cos y – \sin x \sin y$…

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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) –…

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Definition of a Limit

First, here is a video I made about a limit: Understanding what a Limit is. Next, I copy a definition of a limit from [1]. A function $ f(x)$ approaches a limit $ A$…

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The Tangent Line & the Tangent Function

The following equalities provide context to the definition of the tangent function. Now, what if $y$ is a function symbolized by $y(x)$ such that $y(x)=x$? In this case, $x$ is the independent variable…

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