1、2006 S :I 64 o :gIIIII 1, 2, 3, 4, 5, 6, 7 11D16 Z VwpxzMmwtT loMqtoMqw Mo :tmMozfw q :towKlq b1o :exqlogxUMto :pKqMOqpMOqzy = exwqy = logxwUy = xwtoMt 0 tsloMqqtM db aOtzo :wx 0 b :wy = sinx, y = cosx, y = tanxy = xt lo &hwpKxcpbqUzw &hx :wtsloMdsesmwxtMXmwyU 0 oloMTpbfprwOs :Uo :mwTq oO :qxzRw BAT
2、Rw wqpbmzAw witRwimiZ 0 d 0 wqpbV wRwMtx 0 UKloMdAw :wiU 0 oloMiUKloMdw :fq XqtbqzAfw qtMzRwiwOjftloAwstTwit 0 doMww .zmzy R| y = f(x)qsx AU Obfw qtMf(A)q Vbfw f(A) WswpBq XqtOfwo :gqxzB qb :mzBTRw pBw wiyt 0of(g(y) = yU RqjzAw wixt 0og(f(x) = xU RqmqMO Ehbwpb7 sw ETgw g(B)xAw BpsZyssMqU Tbsesg(B)w
3、wift sZyssMTpbMzKqwMw ETAw wiUgtloBwstTwit 0 doMqUzmg(B)xA Bo :2qoqUTblog(B)=Apbtzx1negationslash= x2 Apf(x1)=f(x2)=y BqsloMx1,x2UKlhqbqzx1= g(f(x1) = g(y)=g(f(x2) = x2qslo lbwpzfxAwsiBwsit 0 doMsZysdwqfx1 01 0 pKzKMx opKqtMbMzfU opKyBw wiyt 0of(x)=yqsxUhimiZKwpbTzg(y)=xqbqpo :gqUpVb UThA w :fUo :mh
4、w A G ExzfU opKqpKfwo :xfw f(A) qfw A qb opKfwo :xKqomiZpKqUbYtTbf(x)=ysyzfwytxfwx 0 dsZyssMTpb tfwo :f1q Vb2o :m :ozfUo :mhtxfU opKqU A G EpKq p_hwpzfU pKqVtfU oqMO ElqTbMt?ttMQsMTQoOUMq $psMt soOwpzfw xpKqbfU opKqxx negationslash= y f(x) negationslash= f(y)phx, yS|f(x),f(y)x:swpbTfgwt G UKbfpqKQcx
5、f(y)qMO TyzAwMiZ swVothAU bAz w :U osyz o CT o n pKqUTo :3h1w wox otdb2Mz :fU o CT o n syzxf(y)hxf(x) bpzrjtd w gt Sbpdh3o : Mvb awOtzsinxcosx o Cn pxKdztanxx o CpbUz UpxsXx opxKdlozwo :xKV_ dqpzAprimeUAw BwqVzA qb :TAprime qb :qUpVbAprime iqMyMMiZpbwq MvbqMMb :tmMoxzw MvbqMOloo :mOtoMO3.1 sinxwo :s
6、in xx(2n 1/2),(2n +1/2)p o Cz(2n +1/2),(2n +3/2)po n oMbw p $ $tlq psaw M cx/2,/2pOfpzt Mvhsinxwo :wqo Ym :KMx qz|zArcsinxKMxsin1xq VbArcsinxw x1,1 x/2,/2p o C :pb $1( 1pMO o Cq o n x : :tsloM qdfwq bqVtx o Cn qMMb2ljw txfw UpKqx AKdo :4Oyx1122Oyx11y = Arcsin xy= Arccosx$1:o Ym :( qo(m : wjstzArcsin
7、xwArcxwpbsin xU oww w R t 0o 0 bmw w R )Qwpzotw )QqMOpsinw tArc ZwpxsMTqMb3.2 cosxwo :cosxx(2n1),2np o Cz2n,(2n +1)p o n pbw plq sx0,pOfpzt Mvhcosxwo :wqo(m :KMx qz|zArccosxKMxcos1xq VbArccosxw x1,1 x0,p o n :pb $1 3.3 tanxwo :tanxw xx negationslash=(n +1/2)pzparenleftbig(n1/2),(n +1/2)parenrightbig
8、p o Cpbww plq swx(/2,/2)pOfpzt Mvhtanxwo :wqo Y :KMxqz|zArctanxKMxtan1xq VbArctanxw xR .p x(/2,/2)z o C :pb $2o :5Oyx22y = Arctanx$2:o Y :w4o :w :w loMwpzo :w xo :w OT-D pbOMqtQyzo :U D pKqxTpxsMwpzMVso :w w poxwx lbWbxqoT t qtOg1. D s :fUo :f1mszfprime(x) negationslash=0qsxt 0bf(x) Mof1 D pzy = f(x
9、)tSMo(f1)prime(y)=1fprime(x)U Rqm. f1(y+k)=f1(y)+hqSXqzf1(y)=xswpy+k = f(f1(y)+h)=f(x + h)qsbloh =0qk =0x pzff1 iTh 0qk 0 pblozlimk0f1(y + k)f1(y)k= limh0hf(x + h)f(x)=1fprime(x)pb4.1 Arcsinxw sinprimex = cosxpbUz/2 0swpsinprimex =radicalbig1sin2xo :6qsblozo :w OArcsinprimey =1sinprimex=1radicalbig1
10、sin2x=1radicalbig1y2pb_MOtxqy 8Qoza19 a16Arcsinprimex =11x2a18 a17qsbsSzsinprime(/2) = 0pKqTArcsinxx1p pVd4.2 Arccosxw Arcsin xq 7tlojpVbUz ToToArccosprimex = ArcsinprimexxTpbloza19 a16Arccosprimex = 11x2a18 a17qsb4.3 Arctanxw tanprimex =1/cos2x = 1 + tan2xpbwpzo :w OtArctanprimey =11 + tan2x=11+y2pbxqy 8Qoa19 a16Arctanprimex =11+x2a18 a17qsb
