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浙江大学2000年数学分析考研试题及解答
一、(1)求极限limt01ttt1e1;
1ln(1t1解limt01ttet11limt0etln(1tetelimt0et1t
elimt0etln(1t1ln(1t11tt1ln(1tt
ln(1telimt0tt11elimt01ln(1ttt12elim1tt02t11elimt0t2t(1te2;
或limt01ttttelimt0etln(1teetlimt0ln(1t(1t(1t1ln(1tt2t11
elim1tt0ln(1tt2elimt0(1t21t2telimt0t2t(1t2e2。
(2)设x0a,x1b,xn1212(xn2xn1,求limnxn.解由条件,得xnxn1反复使用此结果
(xn2xn1xn112(xn1xn2,
1n11n1xnxn1((x1x0((ba,n1,2,;
22于是x2n1(x2n1x2n(x2nx2n1(x1x0x0
12n12n1((a