## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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Consider the tangent line that contains the point $(x, c)$. The slope the tangent line to the graph of $f(x)$ at $(x, c)$ can be written as $f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$ Consider $c=0$ and $f(x)=\cos x$. Thus, we have: $f'(0) =\lim\limits_{x \to 0} \dfrac{f(x)-f(0)}{x-0} \\=\lim\limits_{x \to 0} \dfrac{\cos x -\cos 0}{x}\\=\lim\limits_{x \to 0} \dfrac{\cos x-1 }{x}\\=0$