微积分第一章课外习题参考答案(1)(1)(1).pptVIP免费

微积分课外习题参考答案第一章极限与连续预备知识(1-2)111..1.{|30}.2.[1,1],[2,(21)],.111,123.,.111111,0114.,1,.1ln,1xxpxxxkkkZxxxxxxeexxxxxxx一且2231.5.(1),arcsin,.2(2),arctan,.2,026..7.ln,0.,248.()3,0.19.(3)2,(2)1,()2,212().22uxpyuuvvyeuvvxxxxxxxfxxxx22212..,2.33(2)10.[()]0010||1[()]1||11||1hrpVRhhrhrxfgxxxexgfxxxe二三注意作图形.2222..()(2)(22)[2()]2||..()log(1)1loglog(1)1().aaapfxfaxfbaxfbaxTbafxxxxxxxfx四证明:周期五证明§1.1,§1.2数列极限(3-4)13..121(1)(1).(2).232.(1)0.(2)0.(3)2.(4)1.(5).(6).nnnpnnxxnn一填空题.1.不存在不存在3..||||||0lim||||.:(1),lim||1,lim.nnnnnnnnnxpUaUaUaUUU二1.证明由可知例取则但不存在2123211114.2.:,111(1)12222111()22()221312122()22limlim33nnnnnnnnnpPPPP解由题意4.3.:{},0,||,1,2,.0,lim0,,,||,,||||||,lim0.nnnnnnnnnnnnpxMxMnyNnNynNMxyxyxy证明有界使得当时从而,当时21112212222124.4.lim,,,22,||;lim,,,212,||;max{2,21},,||,lim.knkknknnnpxANkNkNxAxANkNkNxANNNnNxAxA证明:>0,由当即当时同理,由当即当+1时取则当时124.5.();(lim(),limlim[()],.)();:(1),(1).();11(1),;(2),.11(),.2nnnnnnnnnnnnnnnnnnnpaxyyxyxbxycxnyxnynndxynn不存在若存在则存在矛盾不一定例不一定例:不一定.例:§1.3-§1.4函数的极限(5-6)101011010100||16..:(),1||1lim()1,lim()1,lim()1;lim()1,lim()1,lim()..lim()1,lim().xxxxxxxxxxpfxxfxfxfxfxfxfxfxx二解设则不存在三不存在(1)(1)(2)(2)(2)6..(1)2,()2cos2(),cos(,).(2)2,,2()(2)cos(2)0,22,cos.,nnnnnpxnyxnnnyxxxnxyxnnxyxx四解:取则在上无...