數(shù)學(xué)分析中題庫(kù)

1、1數(shù)學(xué)分析（中）題庫(kù)一選擇填空（每小題4分，共分）10.設(shè)函數(shù)在可積且平方可積，則的Fourier級(jí)數(shù))(xf][???)(xf_______________收斂于.)(xf11.下列集合是連通緊集的是___________.AB22()|01Sxyxy????22()|1Sxyxy???C.D.221()|12Sxyxy????22()|1Sxyxy???3.函數(shù)的Fourier級(jí)數(shù)在點(diǎn)x=2處收斂于201()110xxfxx????

2、?????__________________________________________4.=__________________________.lim1sin3nnnn????5.的Fourier正弦級(jí)數(shù)在收斂12[0)2()11[1)2xxfxxx???????????32x??于____________6.若冪級(jí)數(shù)在區(qū)間X上收斂，則下列結(jié)論不一定正確的0nnnax????是A它的和函數(shù)在X上連續(xù)B它在X上內(nèi)閉一致收斂；C在

3、X上收斂；D在X上收斂11nnnnax?????101nnnaxn??????7.函數(shù)在點(diǎn)(121)處沿方向______________的2()2fxyzxyz??方向?qū)?shù)取最大值最大值為__________________________.315.函數(shù)在點(diǎn)(11)處沿方向______________的方向?qū)?2)(yxxf??數(shù)取最大值最大值為__________________________.16.集合是緊集當(dāng)且僅當(dāng)_______

4、__________________nSR?17.中點(diǎn)列是基本點(diǎn)列當(dāng)且僅當(dāng)______________________nRnx_________________________________________________________.18.空間曲線在點(diǎn)（1，1，2）處的切線方程為???????????036222222zyxzyx__________________________________________________

5、___________.19.多元函數(shù)在一點(diǎn)的各性質(zhì)之間的關(guān)系為0P?????)()()()((A)連續(xù)(B)可微(C)可偏導(dǎo)；(D)在某鄰域上偏導(dǎo)數(shù)存在且在0P點(diǎn)連續(xù).0P14.判斷(1)f(x)在區(qū)間上可積且平方可積，則f(x)的Fourier級(jí)數(shù)平方][???收斂于f(x).（）(2)f(x)在區(qū)間上連續(xù)，則f(x)的Fourier級(jí)數(shù)收斂于f(x)][???（）.(3)發(fā)散（）????0)1(nnna????nna0lim(4)