1 math253 calculusiii winter 2019 practice final solutions 1 28 pts does the sequence converge or diverge why if it converges what is the limit 3n3 16n a an cos ...
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...Math calculusiii winter practice final solutions pts does the sequence converge or diverge why if it converges what is limit n a an cos solution by examination of leading terms lim since cosisacontinuousfunction wegetlima andthesequenceconverges b this to zero there are many reasonable explana tions and most them use words something naive like switches after vary ingamountsoftime betweentwosequenceswhichbothconvergetozero would bene i probably accept anything not erroneous alternate between word really implies taking turns one can following argument we have so squeeze theorem that limb answer because coulduse butthatistricky c cn en extension function l hopital s rule bounded increases innity d dn diverges examining how ever sum convergent divergent series x do ratio test less than xsin p sin now con verges comparison whichconverges bythep original absolute conver gencetest nn alternates be tween converging never stays close either divergence looking at expect behave which prove for la...