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考研数学公式完整版
高等数学公式
导数公式:
(tgx)??sec2x(ctgx)???cscx(secx)??secx?tgx(cscx)???cscx?ctgx(ax)??axlna(logax)??1xlna2(arcsinx)??11?x21(arccosx)???1?x21(arctgx)??1?x21(arcctgx)???1?x2基本积分表:
?tgxdx??lncosx?C?ctgxdx?lnsinx?C?secxdx?lnsecx?tgx?C?cscxdx?lncscx?ctgx?Cdx1x?arctg?C?a2?x2aadx1x?a?ln?x2?a22ax?a?Cdx1a?x?ln?a2?x22aa?x?Cdxx?arcsin?C?a2?x2a?2ndx2?cos2x??secxdx?tgx?Cdx2?sin2x??cscxdx??ctgx?C?secx?tgxdx?secx?C?cscx?ctgxdx??cscx?Cax?adx?lna?Cx?shxdx?chx?C?chxdx?shx?C?dxx2?a2?ln(x?x2?a2)?C?2In??sinxdx??cosnxdx?0022n?1In?2nxa22222?x?adx?2x?a?2ln(x?x?a)?Cxa2222222x?adx?x?a?lnx?x?a?C?22xa2x2222a?xdx?a?x?arcsin?C?22a三角函数的有理式积分:
2u1?u2x2dusinx?, cosx?, u?tg, dx?
21?u21?u21?u2一些初等函数: 两个重要极限:
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sinxex?e?x lim?1双曲正弦:shx?x?0 x21x ex?e?xlim(1?)?e?2.718281828459045...双曲余弦:chx?x?? x2 shxex?e?x双曲正切:thx??x
chxe?e?x 2arshx?ln(x?x?1)
archx??ln(x?x2?1) 11?xarthx?ln 21?x
·和差角公式: ·和差化积公式:
sin(???)?sin?cos??cos?sin?cos(???)?cos?cos??sin?sin?tg??tg?tg(???)?1?tg??tg?ctg??ctg??1ctg(???)?ctg??ctg?·倍角公式:
sin??sin??2sin???22??????sin??sin??2cossin22??????cos??cos??2coscos22??????cos??cos??2sinsin22cos???sin2??2sin?cos?cos2??2cos2??1?1?2sin2??cos2??sin2?ctg2??1ctg2??2ctg?2tg?tg2??1?tg2?·半角公式:
sin3??3sin??4sin3?cos3??4cos3??3cos?3tg??tg3?tg3??1?3tg2?sintg?2????1?cos??1?cos? cos??2221?cos?1?cos?sin??1?cos?1?cos?sin??? ctg????1?cos?sin?1?cos?21?cos?sin?1?cos?abc???2R ·余弦定理:c2?a2?b2?2abcosC sinAsinBsinC?2
·正弦定理:
·反三角函数性质:arcsinx??2?arccosx arctgx??2?arcctgx
高阶导数公式——莱布尼兹(Leibniz)公式:
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(uv)(n)k(n?k)(k)??Cnuvk?0n?u(n)v?nu(n?1)v??n(n?1)(n?2)n(n?1)?(n?k?1)(n?k)(k)uv?????uv???uv(n)2!k!
中值定理与导数应用:
拉格朗日中值定理:f(b)?f(a)?f?(?)(b?a)f(b)?f(a)f?(?)柯西中值定理:?F(b)?F(a)F?(?)曲率:
当F(x)?x时,柯西中值定理就是拉格朗日中值定理。弧微分公式:ds?1?y?2dx,其中y??tg?平均曲率:K???.??:从M点到M?点,切线斜率的倾角变化量;?s:MM?弧长。?sy????d?M点的曲率:K?lim??.
23?s?0?sds(1?y?)直线:K?0;1半径为a的圆:K?.a定积分的近似计算:
b矩形法:?f(x)?abb?a(y0?y1???yn?1)nb?a1[(y0?yn)?y1???yn?1]n2b?a[(y0?yn)?2(y2?y4???yn?2)?4(y1?y3???yn?1)]3n
梯形法:?f(x)?ab抛物线法:?f(x)?a定积分应用相关公式:
功:W?F?s水压力:F?p?Amm引力:F?k122,k为引力系数
rb1函数的平均值:y?f(x)dxb?a?a12均方根:f(t)dtb?a?a空间解析几何和向量代数:
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考研数学公式完整版(免费版,考研必备)
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