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Investigate the concept of limits and continuity in calculus, including the definition of a limit, techniques for evaluating limits algebraically and graphically, and the properties of continuous functions. Explore the relationship between limits and derivatives, emphasizing the connection between instantaneous rates of change and the behavior of functions at specific points. Additionally, discuss applications of limits in calculus, such as determining the slope of a curve, finding maximum and minimum values, and solving problems in physics, economics, and engineering.
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