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Student Guide:We will not be giving detailed proofs of limit computations. The ideas needed to do this are in section 2.4 of the text, which we will not cover ; you will not be responsible for section 2.4. (This material is covered in detail in an advanced calculus course.) Two important types of tools are developed to calculate limits. One tool depends on algebraic skills, doing things like factoring expressions. The other tool is a limit property of "continuous functions". Combining these two sorts of tools allows one to compute a large variety of limits without drawing pictures or plugging in numbers. We will revisit tangent lines, average and instantaneous velocity using our understanding of limits. This leads to the definition of the derivative.
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