习题课二[数列极限,函数极限]

习题课(二)数列极限,函数极限22221.:11(1)lim;313(2)limsin()0,0.nnNnnnnaa用定义证明332.:lim,lim.nnnnNaaaa用定义证明若则213.:1(1)lim 322; (2)lim1.21xxxx用定义证明42233315.4113(1)lim ( )2_;510052!3 5 1721(2)lim_;2 4 1621(3)lim_;12nnnnnnnnnnnknnnk填空题316.20.,.nnnnxxxnx设数列满足证明收敛 并求其极限收敛证明数列利用不等式设), 2 , 1(1)11ln(11), 2 , 1(ln1211 . 7nnannnnnnna1218. , ,|,1,2,.: ,.nnnnnnnnnncsxscccxxc nsx设为正数列数列满足:证明 若收敛 则也收敛12129.(1)lim,:lim;(2)lim,0(1,2,):lim.nnnnnnnnnnaaaaaanaaana aaa设证明设且证明4.:lim,.nnnnaaaaaa证明对和只有有限个使不成立