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74-hw7 - MATH 74 HOMEWORK 7 DUE MONDAY MARCH 26 A big...

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MATH 74 HOMEWORK 7 - DUE MONDAY, MARCH 26 A big reason people find Math 104 difficult is that they know calculus. If you are too familiar something, it is hard to distinguish what you “really know” from what you are merely familiar with. A good analogy is with language: many native English speakers would score worse on a test of English grammar than non-native speakers because they have never had to think about English grammar. If you are familiar enough with a language you can get by without it. Analysis is the grammar of calculus. To learn it properly you need to re-evaluate a lot of what you know in a critical light. The point of the first four exercises, taken from Solow, is to put you in a critical frame of mind. The point of the remaining exercises is to get you thinking about calculus and symbolic manipulation, hopefully in a fresh way. 1. Do problem 4.14 in Solow. (Don’t write too much.) 2. Look at the proposition and proof in problem 5.9 in Solow. (Ignore his instruc- tions.) Suppose you are grading that proof out of 10. How many points do you give it, and why?
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