2014考研数学三真题答案.doc

2014年全国硕士研究生入学统一考试数学三试题答案一、选择题:1~8小题,每小题4分,共32分,下列每小题给出的四个选项中,只有一项符合题目要求的,请将所选项前的字母填在答题纸...指定位置上.(1)D(2)B(3)(4)D(5)B(6)A(7)(B)(8)(C)二、填空题:9?14小题,每小题4分,共24分,请将答案写在答题纸...指定位置上.(9)pdpdR440??(10)223ln?(11)21?a(12))e(121?(13)[-2,2](14)25n三、解答题:15—23小题,...、证明过程或演算步骤.(15)【答案】22121111111110202211212112???????????????????????????????????uelimuuelimx)e(xlim,xux)e(xlimxtdtdtt)e(lim)xln(xdt]t)e(t[limuuuuxxxxxxxxx则令(16)【答案】432131211112020212021202120212021???????????????????????????????????????????????????????????????????????????????????d)(dsincoscos)dcoscos(dsincoscoscosddsincoscosdsindsincoscosdsincossincosd(17)【答案】ycose)ycose(fxExx????)ycos(e)ycose(fysine)ycose(fyE)ysin(e)ycose(fyEycose)ycose(fycose)ycose(fxExxxxxxxxxx????????????????????22222222ycose)ycose(f)ycose(fe)ycoseE(e)ycose(fyExExxxxxxx??????????????44222222令uycosex?,则u)u(f)u(f????4,故)C,C(,ueCeC)u(fuu为任意常数2122214????由,)(f,)(f0000???得4161622uee)u(fuu????(18)【答案】由13142???????)n)(n()n)(n(limn,得1?R当1?x时,?????031n)n)(n(发散,当1??x时,??????0311nn)n)(n()(发散,故收敛域为),(11?。0?x时,)x(s)x(x))x(xx())xx(x())x(x())dxx)n((x()x)n(x()x)n(()dxx)n()n((x)n)(n(nnnxnnnnnnxnnn???????????????????????????????????????????????????????3223030020201000131231**********。0?x时,3?)x(s,故和函数313)x(x)x(s???,),(x11??(19)【答案】证明:1)因为10??)x(g,所以有定积分比较定理可知,?????xaxaxadtdt)t(gdt10,即????xaaxdt)t(g0。42)令}]dt)t(ga[f)x(f){x(g)x(g]dt)t(ga[f)x(g)x(f)x(F)a(