2011工科數(shù)分第一學(xué)期期中試題答案

1、習(xí)y yx2322ln3(sinx)x(lnsinxxcot5lim(x)4lim(1).(2分xxx3 44)習(xí)y yx2322ln3(sinx)x(lnsinxxcot5lim(x)4lim(1).(2分xxx3 44).(5 分4x4 ex (8分111t11t三.(4分11ttd21t .(8 )1dx1tx0 x 2.(2 分 lim f (x) lim f (x) x 0 lim f(x) x 2 .(5分.(8 分 1 ) limx1lnlim( .(2 分lnxx1 (x1)ln1 lim.(5 分1xlnx(x limx.(6分x1 xlnx x 1 ) limx1lnlim

2、( .(2 分lnxx1 (x1)ln1 lim.(5 分1xlnx(x limx.(6分x1 xlnx x1 .(8分x1 lnx1 2.(9分f(x) 2xcos1 x2(sin 1)x 六x 2xcos1 sin xx.(3 分x3tan2 xx1xtan3 cos2 x f (x) x 3xtan2 tan3 xcos2 (6分x2 cos2 tan3 x tan3 x f (0) x2cos1 lim lim xcos1 0f (0) xf (0) x(9分V 1r2h 1(2Rhh2h 1(2Rh2 h3(3分七333 1(4Rh3h2.(6 分 h 43故當(dāng)h 4R時(shí)V 最(8分

3、3令得由問題的實(shí)際意義f(x) xsin令(1分f (x) 1cosx (2分f(0) 且等號(hào)成立的點(diǎn)是孤立的, f (x單調(diào)增加x 0時(shí) f(x) 即 sinx .(4 分g(x) sin x x3 令(5分g(x) cosx xf(0) 且等號(hào)成立的點(diǎn)是孤立的, f (x單調(diào)增加x 0時(shí) f(x) 即 sinx .(4 分g(x) sin x x3 令(5分g(x) cosx x2 2.(6 分g(x) sinx x 故g(x)單調(diào)增加, 又g(0) 0 故當(dāng)x 0時(shí)g(x) (9分g(x單調(diào)增加, g(0) x 0g(x) 0 , 即 x sinx.(10分limy .(1分lim y

4、.(2分y 8(1y x .(4分y 16(x1)2(x(1 y x 1,x (6分.(10分x1000y拐4,(3)4 50間y1101x(12分limF(x) F(0) 十由題設(shè), .(1分4ln(1x3) 22( 11ln(1x3) 1)13.(3 分44fy1101x(12分limF(x) F(0) 十由題設(shè), .(1分4ln(1x3) 22( 11ln(1x3) 1)13.(3 分44ffxo(x3) (1 o(x3)f(x)cosx f(0) f (0)xx (f(0)1) f (0)x( f(0) 1)x2 f (0) x3 o(x3.(7 分f (0) f (0) f(0)1 f(0) 得4f (0) 2f(0)f (0) f (0) F(x) f十一令.(1 分xlimf f (0) lim f(x) .(2分xxf (x) f F(x) (4分xxf (x)(f(x) f