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# Of functions in the usual and in the polar coordinate

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of functions in the usual and in the polar coordinate system) how to compute volumes of certain solids how to compute integral averages the statement of the Mean Value Theorem and how to use it to estimate integrals Limits and continuity You should know the definition of the limit (and one-sided limit) using the neighborhoods and also ε - δ . the definition of infinite limits and limits at infinity how to apply the definition to prove the existence of the limit (i.e how to do ε - δ proofs) 1

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all the basic limit laws how to apply the limit laws to compute limits the Squeezing Principle the definition of continuity at a given point how to apply the basic limit laws to show the continuity of certain functions (e.g. poly- nomials, rational functions in their domain, etc.) the theorem about the composition of continuous functions the limit of sin x x as x 0 and how to use this to compute other limits Bolzano’s theorem and the Intermediate Value Theorem and how to use them to show that certain equations have solutions the Extreme Value Theorem and how to apply it the definition of uniform continuity Sample practice problems 1. We know that g is integrable on [2 , 7] and R 7 2 g ( x ) dx = 5. Find R 1 0 g (2 x + 5) dx .
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