2001-2008大连理工数学分析考研试题(国外英语资料).docVIP

2001-2008大连理工数学分析考研试题(国外英语资料) 2000, from the first to the following eighth questions, select 6 questions, 10 points for each question 1. proof: 1 (FX) X In interval 0 ((1)) (001 of which) uniformly continuous, but not within (0,1) Uniform continuity 2. proof: if () [[]] Fxab in monotone, then () [[]fxabRiemann) is integrable inside 3. proof: Dirichlet function: 0, () One (). X FX P X QQ ? ? ? ? ? ? ? Irrational number A rational number is continuous at all irrational points and interrupted at a rational point 4. proof: if (), (,), ()) FxCabab? (referring to the continuous function) and any (or), (,), AB,,,,,,,,,,,,,,,,,,,, 0fxdx? ?? Then () 0 FX, (or) XAB? 5. proof: 1 (0), 0, [,] nx NNE ??? ? Inconsistent convergence, but for uniform convergence Convergence 6. proof: 41 Sin, 0 () 0,0 XX FX X X ? ? ? ? ? ? ? In? There is a continuous two order derivative at x=0 7., the volume of ellipsoid of 3.5, long axis, a, B and C is calculated by the method of multiple integral 8., calculate second types of surface integrals: xdydzydzdxzdxdy???, among them, And, 0,1, xyzxyzxyz??? Its a triangle (). The direction of the law is exactly the same as the axis. Two. Choose 4 questions from the 9-14 questions 9. hypothesis 12 22... Lim, Lim 2n N Nnaana A AA N?????? Proof?: 10. calculate the integral: 22xdyydx I XY?? ? In which?, For gamma contains the origin of a piecewise smooth closed curve, Take the right direction. 11. calculate the surface integral 333 SIxdydzydzdxzdxdy S ellipsoid 222 Two thousand two hundred and twenty-one XYZ ABC The??? Outside。 12. set 1 1 () 0, [1,1], () 1,1,2,3,....nnnxCxdxn???????, for any C0 ([1), [], 1]nxcc??? In the uniform convergence in 0. Proof: for any () [1,1]gxC?: LIM () () (0) n Ngxxg??? 13., it is proved that the discontinuity point of a strictly increasing function can only be the breakpoint between the first class 14. (,) (()) [,,,,,,,,, ()) FxyabIyfxydx? ????? in succession, on [...] YAB convergence, but, (), fxbdx? Hair??? Scatter, prove, [(]