# sol4 - Problem Set 4 Calculus 1 Abdullah Khalid Hassan...

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Problem Set 4 Calculus 1 Abdullah Khalid, Hassan Bukhari December 8, 2010 Thomas’ Calculus, Chapter 2 Additional and Advanced Exercises 18. The Dirichlet ruler function, f ( x ), is discussed in detail in Spivak on pages 97-98 of Chapter 5. Basically he shows that for every a (0 , 1), lim x a f ( x ) = 0. Now parts (a) and (b) of this question are easy consequences of this fact from Spivak. Spivak also draws this function. So essentially the point of giving you this question was two-fold. To make you understand pages 97-98 of Spivak. To convince you that Spivak is not “impossible” (as many of you believe). Thomas at its best has ingredients of Spivak in it! 19. Consider θ ( l ) to be the temperature at the equator at longitude l . Deﬁne a function f ( l ) = θ ( l ) - θ (180 + l ) (We are assuming that longitude varies form 0 to 360 ). Either f (0) = 0 and we are done. Else f (0) = a 6 = 0. However f (180) = - a . Hence between 0 and 180 we have gone from a to - a . By Theorem 1 of Chapter 7 of Spivak, there exists

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## This note was uploaded on 01/10/2011 for the course EE 100 taught by Professor Razasuleman during the Spring '10 term at University of Engineering & Technology.

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sol4 - Problem Set 4 Calculus 1 Abdullah Khalid Hassan...

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