This lecture notes provide a clear, step-by-step introduction to the conceptual and notational foundations of limits in calculus. It begins by formally defining what a limit is, stating precisely the behavior of a function as its input approaches a given number. Helpful illustrations and examples are then used to explain specialized limit notations - representing one-sided and two-sided limits with arrow symbols. This visual approach aids intuition on how functions can tend towards limits from different directions. The lecture notes then outline a systematic numerical method to estimate limits based on tabulating function values as the inputs get arbitrarily close to the limit point. Detailed solutions demonstrate this approach before specific practice problems are provided, covering a variety of function types like polynomials, radicals, and rational functions. The accessible style, real-world examples and emphasis on numerical estimation techniques make this an excellent resource for getting an initial sense of limits and for building skill in evaluating limits computationally. Going through the illustrated explanations and working through the example problems would prepare students well for grasping this vital introductory concept in calculus.
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