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Hida, Rogawski
. ImproperIntegrals areonesthatinvolve \"infinite\"boundsinxory(orboth) Iftheintegralhasavalue,wesayit \\ . . . 1 CONVERGES.Otherwiseit DIVERGES. ,
Homeworktonight:45minutesofpracticefromtheAPreviewofch2inRogawski
Asfaraslogisticgrowthyouneed tobeabletorecognizetheslope fieldandthedifferentialequationthat leadstoalogisticfunction.Youalsoneed tobeabletowritealogisticfunction fromadifferentialequationasfollows:
y 6 5 4 3 2 1 6 5 4 3 2 1 0 1 2 3 4 5 6 x 1 2 3 4 5 6
y 6 5 4 3 2 1 6 5 4 3 2 1 0 1 2 3 4 5 6 x 1 2 3 4 5 6
Answer key No.3 to selected homework problems: Math. 110B 8.3 1. Count the number of 4subsets of the set {1, 2, 3, 4, 5, 6}: C(6, 4) = ( 6 ) = 4 15. The 4cycle (1234) generates a cyclic subgroup {I, (1234), (12)(34), (4321)}. Another 4cycle (1324) (m
Answer key No.2 to selected homework problems: Math. 110B 7.6 1. aK = K means ae = k K; so, a K. Conversely, if a K, then ak K for all k K because K is a subgroup. This shows aK K. Pick any k K, then k = ek = (aa-1 )k = a(a-1k) aK, because K
Answer key No.1 to selected homework problems: Math. 110B 7.1 2. A permutation f either fixes one number 1 j 3 or two numbers or moves all. There are 3 elements fixing only one number (those interchanging the two numbers different from j). For such