习题3.4 1.
(1)f?(x)?2x(2)dy?0.04(3)f(1.02)?f(1)?0.0402
2.
(1)f?(x)??1x2(2)dy??0.05(3)f(?0.95)?f(?1)??0.0526316
3.
(1)f?(x)?sinx?xcosx;dy?(sinx?xcosx)dx22(2)f?(x)?2xcosx?xsinx;dy?(2xcosx?xsinx)dx1(3)f?(x)?x(4)f?(x)?sinx?lnxcosxsinx221;dy?(xsinx?lnxcosxsinx222)dx2xsinx?(x?1)cosxsinx222;dy?(2xsinx?(x?1)cosxsinxxx(5)f?(x)?e(sinx?cosx);dy?(e(sinx?cosx))dx(6)f?(x)?6x(x?cosx)?(3x?1)(2x?sinx)(x?cosx)222222dy?(6x(x?cosx)?(3x?1)(2x?sinx)(x?cosx)11?x2)dx22(7)f?(x)?2xtanx?xsecx?dy?(2xtanx?xsecx?2211?x2)dxx1?x22
xx2(8)f?(x)?ecotx?ecscx?arctanx?dy?(ecotx?ecscx?arctanx?xx2x1?x)dx4.
(1)10?3.1667(2)99.7?9.985
5.
(1)e?x?1,f(x)?e,?x?x,x0?00f(0?x)?f(0)?f?(0)x?e?x?1?x,xxx
(2)sinx?x,f(x)?e,?x?x,x0?0f(0?x)?f(0)?f?(0)x?0?xcos0?x6.
p?(x)??14x?7
p(26)?p(24)?2p?(24)?27.
?p?500p?x?10000?500?0.3?12xx?10000?0.75
8.
?p?500p?x?10000??1.2x1(0.02x?1)22500x?10000?0.000012
9.
(1)为正(2)f?(100)?2广告支出100千元时，每增加一千元广告，收入增加2千元；f?(100)?0.5广告支出100千元时，每增加一千元广告，收入增加0.5千元；
(3)由(2)的结论知，若f?(100)?2，增加广告，即略多于1000000元广告费。f?(100)?0.5，减少广告，即略少于1000000元广告费。10. 略