考研數(shù)學(xué)三知識點總結(jié)

1、高數(shù)高數(shù)三角函數(shù)變換cos(A?B)=cosAcosBsinAsinBcos(AB)=cosAcosBsinAsinBsin(A?B)=sinAcosB?cosAsinBsin(AB)=sinAcosBcosAsinBsinAcosB=12[sin(AB)sin(A?B)]sinxcosx=12sin2xsinAsinB=12[cos(A?B)?cos(AB)]sin2x=12(1?cos2x)cosAcosB=12[cos(A?B)c

2、os(AB)]cos2x=12(1cos2x)cos2x=1?tan2x1tan2xsin2x=2tanx1tan2xarcsinxarccosx=π2arctanxarccotx=π2arctanxarctan1x=π2圓柱體積V=πr2h圓錐體積V=13πr2h球體積V=43πr3橢圓面積S=πab拋物線y2=2px交點坐標(biāo)(p20)準(zhǔn)線x=?p2點到直線距離∣ax0by0c∣√a2b2第一類間斷點：包括可去間斷點和跳躍間斷點?？扇?/p>

3、間斷點：間斷點處左右極限存在但不等于該點函數(shù)值。f(x00)=f(x0?0)≠f(x0)跳躍間斷點：間斷點處左右極限存在但不相等。f(x00)≠f(x0?0)第二類間斷點：間斷點處左右極限至少有一個是∞重要極限limx→0sinxx=1limx→∞(11x)x=elimx→0(1x)1x=ex趨向于0時的等價無窮小sinx～xtanx～xarcsinx～xarctanx～x1?cosx～12x2∫0af(x)dx=12∫0a[f(x)f

4、(?x)]dx∫?aaf(x)dx=∫0a[f(x)f(?x)]dxfx(xy)fy(xy)在(x0y0)連續(xù)?z=f(xy)在(x0y0)可微?f(xy)在(x0y0)連續(xù)二重積分特點積分區(qū)域D關(guān)于x軸對稱?Df(xy)dσ=0f為y的奇函數(shù)，即f(x?y)=?f(xy)?Df(xy)dσ=2?D1f(xy)dσf為y的偶函數(shù)，即f(x?y)=f(xy)積分區(qū)域D關(guān)于y軸對稱?Df(xy)dσ=0f為x的奇函數(shù)，即f(?xy)=?f(

5、xy)?Df(xy)dσ=2?D1f(xy)dσf為x的偶函數(shù)，即f(?xy)=f(xy)積分區(qū)域關(guān)于原點對稱?Df(xy)dσ=0f為x，y的奇函數(shù)，即f(?x?y)=?f(xy)?Df(xy)dσ=2?D1f(xy)dσf為x，y的偶函數(shù)，即f(?x?y)=f(xy)函數(shù)展開式ex=1x12!x21n!xn=∑k=0nxkk!sinx=x?13!x315!x5?(?1)n?11(2n?1)!x2n?1=∑k=0n(?1)kx2k1(