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Why do we separate the instantaneous from the average of any given variable (velocity, for example) and how do limits relate to the tangent problem

Why do we separate the "instantaneous" from the "average" of any given variable (velocity, for example) and how do limits relate to the tangent problem and the area problem. I have been looking all over the internet and my book and cannot find any relevant information. PLEASE HELP!!! :,(

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