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As a teacher, I would like to teach approximation techniques almost/specially from the very beginning in the courses of introductory physics. I would like to give at least some examples here and there where mathematical approximations are required or at least greatly reduces the work needed to solve the problem at hand. But such examples are not that common in the standard textbooks.

So, I'm here for advices and to hear other people experiences. How do you handle approximating results when teaching introductory course of physics?