山東警察學(xué)院《高等數(shù)學(xué)》2017-2018學(xué)年期末試卷

山東警察學(xué)院《高等數(shù)學(xué)》2017-2018學(xué)年第一學(xué)期期末試卷題次一二三得分評(píng)卷人1.設(shè)z=xsiny2,則=siny2,=2xycosy2.EQ\*jc3\*hps23\o\al(\s\up23(z=),xfu)EQ\*jc3\*hps23\o\al(\s\up23(u),v)EQ\*jc3\*hps24\o\al(\s\up23(具),3f)EQ\*jc3\*hps24\o\al(\s\up23(二),,v)EQ\*jc3\*hps24\o\al(\s\up23(偏),fu)EQ\*jc3\*hps24\o\al(\s\up23(數(shù)),,v)EQ\*jc3\*hps23\o\al(\s\up23(=),yf)EQ\*jc3\*hps23\o\al(\s\up23(v),u,)EQ\*jc3\*hps23\o\al(\s\up10(-),n)4.點(diǎn)M的直角坐標(biāo)(x,y,z)與柱面坐標(biāo)(p,θ,z)的關(guān)系為 x=pcosθ,y=psinθ,z=z.在柱面坐標(biāo)下,體積元素dv=pdpdθdz.dx,nn12.訂不要答題不要答題2e2x+x. 2x+2y 2（8分,）.已知z=f(x,y)是由方程x2+y2EQ\*jc3\*hps23\o\al(\s\up8(δ),δ)EQ\*jc3\*hps23\o\al(\s\up8(z),x)EQ\*jc3\*hps23\o\al(\s\up8(δ),δ)EQ\*jc3\*hps23\o\al(\s\up10(2z),x2)FxEQ\*jc3\*hps23\o\al(\s\up6(δ),δ)EQ\*jc3\*hps13\o\al(\s\up12(2),x)EQ\*jc3\*hps23\o\al(\s\up6(z),2)EQ\*jc3\*hps23\o\al(\s\up6(x),z)(2z)2+x2(2z)2+x2Dxydσ=1xxydyD12()dx解:設(shè)L所圍的區(qū)域?yàn)镈(xyx2)dx+xy2dy=(y2+x2)dxdyLD02πdθ02p3dp訂答題1（‘(n+1)n+12n.n!n2.（‘分）求冪級(jí)數(shù)nEQ\*jc3\*hps23\o\al(\s\up7(1),2)EQ\*jc3\*hps23\o\al(\s\up7(d),d)EQ\*jc3\*hps23\o\al(\s\up7(y),x)x2的通解.解:令y=ux,則dx2分4.（8分）求一曲線的方程,這曲線經(jīng)過原點(diǎn),并且它在點(diǎn)(x,y)處的切線斜率等于2x+y.dx2xexdx+C]x.[2xex2ex+C]5、（10分）設(shè)z=f(x,y)滿足條件：=5-2y-x2，=y-2x，且f(0,0)=1.求f(x,y)的極值.|lfy|lfy,得駐點(diǎn)(1,2),(-5,-10)A=fxx=-2x,B=fxy=-2,C=fyy=1在點(diǎn)(1,2)處,AC-B2=-6<0,f(1,2)在點(diǎn)(-5,