高等数学基础知识点大全.pdf

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2、x?C?x|x?A?B?A?B?2?C?(x,y)|y=x?y?x?D=(x,y)|?2x-y=1,x+4y=5?C?D?3?A=x|1?x?3?B?x|(x-1)(x-a)=0?B?A?a?A?B?4?A?B?C?5?A?1?2?3?4?n?B?2?4?6?8?2n?a?b a?b?a?b?a?b?b?a?3/96 a?(-?b)?(-?,?0.?x-?y?y=f(x)?y=F(x)?f?F?a)?x2+y2=r2 b)?c)?I I?f(x)?f(x)?I I?cosx?(-?,+?.?(a,b)?(a,b)?x1?x2?x1?x2?(a,b)?4/96 ?(a,b)?(a,b)?x1?x

3、2?x1?x2?(a,b)?=x2?(-?,0)?(0,+?=?=-=-?l l?l l?tgx?y0?x0?.?(a?b)?R R?R R?).?)?y=x2?(-?,+?0,+?).?x=.?(-?,+?5/96 ?x=?y=x2?).?y=x?y=x?(-?,+?6/96 ?a):?,y?;b):?x=0?,y=1.?a):?(1,0)?b):?(0,1)?(-,+?.?a=m/n a):?,y?;b):?m,n?,y?;c):?,y?(-?,0)?.?)?a):?b):?)?a):?-?/2,?/2?,?.?.?)?7/96 ?a)?:(-?,+?b)?c)?a)?:(-?,+?b)?

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5、x0?.?12/96 ?,x?(x?x0?x0?(x?x0?x0?x0?x0?x0?x0?x)?A?.?.?13/96 ?e=2.718281828459045.?.?.?x=-2t?1/x?0.?y=?x=x0?N N?y=?N N?M?14/96 ?M?.?)?0 0?0 0?.?a)?b)?c)?.?x0?a)?b)?c)?)?3x?x2?3x?sinx?15/96 ?.?1.?sinax?ax?tanbx?bx?2.?x1?x2?x2-x1?x=x2-x1?.?x0?x0?x0+?x?16/96 ?x0?x0?x0?x0?.?.?(a,b?b?a,b)?a?.?(a,b)?(a,b)?

6、a?b?.?.?a)?x0?b)?x0?c)?x0?17/96 ?x=0?-1?+1?x=0?x=0?x=0?:?x0?x0?.?.?x0?x0?x0?x0?18/96 ?a)?b)?c)?-1,1?x0?u=a?x0?u=e?x=x0?u=u0?x=x0?.?.?19/96 ?)?y=sinx?0?x=?/2?0?x=3?/2?-1?0?a?b?x x?x x?t t?t0?t0?t0?t0?t0?t0?=?x0?x0?x(x+?x0?x0?x0?(a,b)?(a,b)?(a,b)?20/96 ?x=x0?x=x0?x0?x0?).?21/96 ?!?=?2x?22/96 ?.?.?.?23

7、/96 ?v(t)?s(t)?(n-1)?.?=a?=0?24/96 ?y=sinx?y=1+3x?.?F(x,y)=0?F(x,y)=0?y.?F(x,y)=0?a)?F(x,y)=0?b)?F(x,y)=0?=?x=0?x=0?y=0.?25/96 ?x0?x0?x0?26/96 ?x0?x0?x0?x0?dy?dy?x?dy?dy.?dx,?27/96 ?dy?du?dy?2x+1?)?28/96 ?x3?.?1.025(?1.024695)?29/96 ?(a?b)?(a,b)?(a,b)?AB?AB?P(x=c)?a,b?(a,b)?(a,b)?a,b?(a,b)?(a,b)?17?

8、30/96 ?a?b?(a?b)?(a?b)?0?1?(0,1)?a(?31/96 ?(LHospital)?(LHospital)?(LHospital)?(LHospital)?a(?N)?=?(LHospital)?32/96 ?33/96 ?),?).?.?a,b?(a,b)?.a)?(a,b)?a,b?b)?(a,b)?a,b?.?.?)?(0,?(-?,0)?x=1?x=2?x=1?x=1?.?34/96 ?x=1?x(x=1?x=2?),?(a,b)?x0?(a,b)?.?x0?x(x0?x0?x(x0?.?x0?.?x0?x0?x0?x0?x0?x0?x0?a)?35/96 b

9、)?c)?x=-2?-4/5?x0?.?a)?x0?b)?x0?c)?=0?.?36/96 ?a,b?(a,b)?-3?3/2?x=1?37/96 ?I?I?(a,b)?(a,b)?(a,b)?38/96 ?(a,b)?a,b?(a,b)?a,b?(0,+?(a,b)?(1)?(2)?=0?(a,b)?(3)?(2)?x0?x0?=0?x=0?2/3?39/96 ?2/3?f(x)?F(x)?dF(x)=f(x)dx?F(x)?f(x)?sinx?cosx?f(x)?F(x)?f(x)?F(x)=f(x)?F(x)+C(C?f(x)?f(x)?.?f(x)?f(x)?F(x)?f(x)?f(x

10、)?F(x)+C.?:=F(x)+C?40/96 ?.?=?1?2?f(u)?F(u)?u=g(x)?Fg(x)?fg(x)g(x)?.?:?u=2x?cos2x=cosu?du=2dx?x=g(t)?g(t)?fg(t)g(t)?(t)?g(x)?f(x)?.(?g(x)?x=g(t)?:?.?x=asint(-?/2t?/2)?dx=acostdt,?41/96 ?u=u(x)?v=v(x)?(uv)=uv+uv?uv=(uv)-uv?u=x?dv=cosxdx?du=dx?v=sinx?dv?dv?(1)v?(2)?42/96 ?u=tan(x/2)?x=u2+1?dx=2udu?43/

11、96 ?y=f(x)?x=a?x=b?A.?f(x)?a,b?a,b?a,b?f(x)?a,b?a,b?a=x0 x1.xn-1xn=b?a,b?x0?x1?.xn-1,xn,?xi-1,xi?i(xi-1?xi),?f(?i)?f(?i)?xi?a,b?S?f(x)?a,b?f(x)?f(x)?a,b?f(x)?a,b?f(x)?a,b?f(x)?a,b?44/96 ?(1)?.?(2)?.?(3)?a,b?f(x)?g(x)?aa.?f(x)?a,+?=.?47/96 ?f(x)?(-?b?a0?f(x)?(a,b?48/96 ?.?.?f(x)?a,b)?0?f(x)?a,b?c(ac0

12、)?x=a?49/96 ?(?/2?x?z.?x,y,z.?x,y,z?x,y?x,y,z?M(x,y,z).?x,y,z?50/96 ?.?yOz?x=0?zOx?y=0?y=z=0?x=y=z=0?M1(x1,y1,z1?M2(x2,y2,z2?A(4,3,1),B(7,1,2),C(5,2,3)?ABC?.?ABC?P1?P2?Ox,Oy,Oz?,0?,0?.?51/96 ?A?C.?52/96 ?L1?L2?L?L1 1?L?L2 2?.?L1?L2?L1?L2?53/96 ?Po(x0,y0,z0),?A,B,CA2+B2+C2?n?3?-4?8?(2,1,-4)?.?Ax+By+C

13、z+D=0.?x,y,z?Ax+By+Cz=0.?By+Cz+D=0.?Ax+Cz+D=0.?Ax+By+D=0.?54/96 By+Cz=0.?Ax+Cz=0?Ax+By=0.?Ax+D=0?By+D=0?Cz+D=0.?l,m,n?Po(x0,y0,z0),?55/96 ?(x,y,z)?x,y,z?56/96 ?r,h?z=f(x,y).?D?57/96 ?D(?.?,y?0.?xOy?z=f(x,y)?M(x,y)?xOy?MP,?(x,y)?z=f(x,y)?z=f(x,y)?xOy?z=f(x,y)?y?xOy?(x,y)?(x,y)?f(x,y)?f(x,y)?(x,y)?58/

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15、,y)?f(x,y)?z=f(x,y)?(x0,y0?y0?x0?z=f(x,y)?)?xz=f(x0?x)-f(x0,y0).?x?z=f(x,y)?(x0,y0?fx(x0,y0?z=f(x,y)?(x0,y0?y0?z=f(x,y0?x0?x0?y,?60/96 ?z=(x,y)?(x0,y0?.?.?fy(x0,y0?z=f(x,y)?(x0,y0?fx(x0,y0?fy(x0,y0?f(x,y)?(x0,y0?f(x,y)?f(x,y)?D?(x,y)?x(?y)?f(x,y)?x(?y)?z=x2siny?.?.?61/96 ?.?z=f(x,y)?fx(x,y)?fy(x,y)?

16、z=f(x,y)?fxx?fxy?fyx?fyy.?fxy?fyx?.?fxy?fyx?fxy?fyx?.?z=f(x,y)?fx(x,y),fy(x,y)?x,?fx(x,y)?x+fy(x,y)?y?()?z=f(x,y)?(x,y)?x,?y)?62/96 ?dz=fx(x,y)?x+fy(x,y)?y?z=fx(x,y)?x+fy(x,y)?y+?)?(x0,y0?(x0?x,y0?y)?(x0,y0?(x0,y0?y)?(x0?x,y0?y).?fx(x,y),fy(x,y)?z=f(x,y)?(x,y)?z=F(u,v)?(u,v)?,?(x,y)?63/96 ?z=f(u,v)?.?.?64/96 ?:?z=u2?u=cosx?v=sinx?u=cosx?v=sinx?(x0,y0?(x,y)?f(x,y)?f(x0,y0)?f(x,y)?(x0,y0?f(x0,y0?f(x,y)?f(x0,y0)?f(x,y)?(x0,y0?f(x0,y0).?(x0,y0?.?(x?(x0 0,y,y0 0?.?.?(x,y)?f(x,y)?65/96 ?z=f(x,y)?(x0,y