锟斤拷锟斤拷锟斤拷锟脚很讹拷锟酵�锟絎(xu锟斤拷)同锟絎(xu锟斤拷)锟斤拷锟角非筹拷锟斤拷锟絇(gu锟斤拷n)锟侥高匡拷锟斤拷(sh锟斤拷)锟絎(xu锟斤拷)锟斤拷锟斤拷些锟截匡拷锟斤拷知锟絉(sh锟斤拷)锟絚(di锟斤拷n)锟斤拷锟斤拷锟斤拷锟斤拷锟角高匡拷锟斤拷(sh锟斤拷)锟絎(xu锟斤拷)锟截匡拷知锟絉(sh锟斤拷)锟絚(di锟斤拷n)锟絯锟絳锟斤拷一锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷1锟竭匡拷锟斤拷(sh锟斤拷)锟絎(xu锟斤拷)锟截匡拷知锟絉(sh锟斤拷)锟絚(di锟斤拷n)

锟斤拷锟斤拷1锟斤拷锟紸锟斤拷锟絯:

锟斤拷锟斤拷锟斤拷锟斤拷e:2πRr+2πRh锟絯锟絜:πR2h(R锟斤拷A锟斤拷锟絯锟斤拷锟铰底圓锟诫徑,h锟斤拷A锟斤拷锟絯锟斤拷)

锟斤拷锟斤拷2锟斤拷锟紸锟紽锟絯:

锟斤拷锟斤拷锟斤拷锟斤拷e:πR2+πR[(h2+R2)锟斤拷平锟斤拷锟斤拷]锟絯锟絜:πR2h/3(r锟斤拷A锟紽锟絯锟酵圓锟诫徑,h锟斤拷锟斤拷锟�,

锟斤拷锟斤拷3锟斤拷锟斤拷锟斤拷锟絯

锟斤拷锟斤拷a-邊锟絃(zh锟斤拷ng),S=6a2,V=a3

锟斤拷锟斤拷4锟斤拷锟絃(zh锟斤拷ng)锟斤拷锟絯

锟斤拷锟斤拷a-锟絃(zh锟斤拷ng),b-锟斤拷,c-锟斤拷S=2(ab+ac+bc)V=abc

锟斤拷锟斤拷5锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷S-锟斤拷锟斤拷eh-锟斤拷V=Sh

锟斤拷锟斤拷6锟斤拷锟斤拷锟紽

锟斤拷锟斤拷S-锟斤拷锟斤拷eh-锟斤拷V=Sh/3

锟斤拷锟斤拷7锟斤拷锟斤拷锟絖(t锟斤拷i)

锟斤拷锟斤拷S1锟斤拷S2-锟较★拷锟铰碉拷锟斤拷eh-锟斤拷V=h[S1+S2+(S1S2)^1/2]/3

锟斤拷锟斤拷8锟斤拷锟組锟斤拷锟絯

锟斤拷锟斤拷S1-锟较碉拷锟斤拷e,S2-锟铰碉拷锟斤拷e,S0-锟叫斤拷锟斤拷e

锟斤拷锟斤拷h-锟斤拷,V=h(S1+S2+4S0)/6

锟斤拷锟斤拷9锟斤拷锟紸锟斤拷

锟斤拷锟斤拷r-锟阶半徑,h-锟斤拷,C—锟斤拷锟斤拷锟斤拷锟絃(zh锟斤拷ng)

锟斤拷锟斤拷S锟斤拷—锟斤拷锟斤拷e,S锟斤拷(c锟斤拷)—锟斤拷(c锟斤拷)锟斤拷e,S锟斤拷—锟斤拷锟斤拷eC=2πr

锟斤拷锟斤拷S锟斤拷=πr2,S锟斤拷(c锟斤拷)=Ch,S锟斤拷=Ch+2S锟斤拷,V=S锟斤拷h=πr2h

锟斤拷锟斤拷10锟斤拷锟斤拷锟侥圓锟斤拷

锟斤拷锟斤拷R-锟斤拷A锟诫徑,r-锟斤拷(n锟斤拷i)锟紸锟诫徑h-锟斤拷V=πh(R^2-r^2)

锟斤拷锟斤拷11锟斤拷直锟紸锟紽

锟斤拷锟斤拷r-锟阶半徑h-锟斤拷V=πr^2h/3

锟斤拷锟斤拷12锟斤拷锟紸锟絖(t锟斤拷i)

锟斤拷锟斤拷r-锟较底半徑,R-锟铰底半徑,h-锟斤拷V=πh(R2+Rr+r2)/3

锟斤拷锟斤拷13锟斤拷锟斤拷

锟斤拷锟斤拷r-锟诫徑d-直锟斤拷V=4/3πr^3=πd^3/6

锟斤拷锟斤拷14锟斤拷锟斤拷缺

锟斤拷锟斤拷h-锟斤拷缺锟斤拷,r-锟斤拷霃�,a-锟斤拷缺锟阶半徑V=πh(3a2+h2)/6=πh2(3r-h)/3

锟斤拷锟斤拷15锟斤拷锟斤拷锟絖(t锟斤拷i)

锟斤拷锟斤拷r1锟斤拷r2-锟斤拷锟絖(t锟斤拷i)锟斤拷锟斤拷锟铰底半徑h-锟斤拷V=πh[3(r12+r22)+h2]/6

锟斤拷锟斤拷16锟斤拷锟紸锟絟(hu锟斤拷n)锟絯

锟斤拷锟斤拷R-锟絟(hu锟斤拷n)锟絯锟诫徑D-锟絟(hu锟斤拷n)锟絯直锟斤拷r-锟絟(hu锟斤拷n)锟絯锟斤拷锟斤拷霃絛-锟絟(hu锟斤拷n)锟絯锟斤拷锟斤拷直锟斤拷

锟斤拷锟斤拷V=2π2Rr2=π2Dd2/4

锟斤拷锟斤拷17锟斤拷桶锟斤拷锟絯

锟斤拷锟斤拷D-桶锟斤拷直锟斤拷d-桶锟斤拷直锟斤拷h-桶锟斤拷

锟斤拷锟斤拷V=πh(2D2+d2)/12,(母锟斤拷锟角圓锟斤拷锟斤拷,锟紸锟斤拷锟斤拷桶锟斤拷锟斤拷锟斤拷)

锟斤拷锟斤拷V=πh(2D2+Dd+3d2/4)/15(母锟斤拷锟角掞拷锟斤線锟斤拷)

锟斤拷锟斤拷2锟竭匡拷锟斤拷(sh锟斤拷)锟絎(xu锟斤拷)锟截匡拷锟斤拷式知锟絉(sh锟斤拷)锟絚(di锟斤拷n)

锟斤拷锟斤拷1.锟絤锟矫條锟斤拷锟斤拷[直锟斤拷锟絕锟斤拷锟絚(di锟斤拷n)]锟斤拷锟斤拷锟斤拷ecosA=(x-1)/(x+1)锟斤拷锟斤拷锟斤拷A锟斤拷直锟斤拷锟絚锟斤拷锟絚(di锟斤拷n)锟斤拷锟斤拷锟絊锟紸锟斤拷锟斤拷锟斤拷锟絁锟斤拷锟斤拷

锟斤拷锟斤拷x锟斤拷锟斤拷x锟斤拷锟斤拷锟斤拷須达拷锟斤拷1锟斤拷注锟斤拷锟斤拷锟斤拷式锟絤锟斤拷一锟叫圓锟紽锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷c(di锟斤拷n)锟斤拷(n锟斤拷i)锟斤拷(指锟斤拷锟角斤拷锟絚(di锟斤拷n)锟斤拷锟斤拷锟截撅拷锟斤拷锟斤拷)锟斤拷锟斤拷該锟斤拷式;锟斤拷锟斤拷锟斤拷(锟斤拷锟絚(di锟斤拷n)锟斤拷锟斤拷锟截撅拷锟斤拷锟斤拷锟絃(zh锟斤拷ng)锟斤拷锟斤拷)锟斤拷锟斤拷邊锟斤拷(x+1)/(x-1)锟斤拷锟斤拷锟斤拷锟斤拷變锟斤拷

锟斤拷锟斤拷2.锟斤拷锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟斤拷锟皆嗭拷锟絵(記锟斤拷锟斤拷锟斤拷(g锟斤拷))锟斤拷

锟斤拷锟斤拷(1)锟斤拷f(x)=-f(x+k)锟斤拷锟絫T=2k;

锟斤拷锟斤拷(2)锟斤拷f(x)=m/(x+k)(m锟斤拷锟斤拷0)锟斤拷锟絫T=2k;

锟斤拷锟斤拷(3)锟斤拷f(x)=f(x+k)+f(x-k)锟斤拷锟絫T=6k锟斤拷注锟斤拷锟絚(di锟斤拷n)锟斤拷a.锟斤拷锟节猴拷锟斤拷(sh锟斤拷)锟斤拷

锟斤拷锟斤拷锟斤拷锟节憋拷?z锟斤拷)o锟斤拷b.锟斤拷锟节猴拷锟斤拷(sh锟斤拷)未锟截达拷锟斤拷锟斤拷小锟斤拷锟斤拷锟斤拷锟界：锟斤拷锟斤拷(sh锟斤拷)锟斤拷锟斤拷(sh锟斤拷)锟斤拷c.锟斤拷锟节猴拷锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟节猴拷锟斤拷(sh锟斤拷)未锟斤拷锟斤拷锟斤拷锟节猴拷锟斤拷(sh锟斤拷)锟斤拷锟界：y=sinxy=sin锟斤拷x锟斤拷硬锟斤拷锟斤拷锟斤拷诤锟斤拷锟�(sh锟斤拷)锟斤拷

锟斤拷锟斤拷3.锟絇(gu锟斤拷n)锟节岋拷(du锟斤拷)锟絈锟斤拷锟絵(锟給锟斤拷(sh锟斤拷)锟剿搞不锟斤拷锟侥嗭拷锟絵)锟斤拷锟結(ji锟斤拷)锟斤拷锟铰ｏ拷

锟斤拷锟斤拷(1)锟斤拷锟斤拷R锟斤拷(锟斤拷同)锟組锟姐：f(a+x)=f(b-x)锟斤拷锟斤拷锟�锟斤拷锟斤拷(du锟斤拷)锟絈锟絊锟斤拷x=(a+b)/2

锟斤拷锟斤拷(2)锟斤拷锟斤拷(sh锟斤拷)y=f(a+x)锟絚y=f(b-x)锟侥圖锟斤拷锟絇(gu锟斤拷n)锟斤拷x=(b-a)/2锟斤拷(du锟斤拷)锟絈

锟斤拷锟斤拷(3)锟斤拷f(a+x)+f(a-x)=2b锟斤拷锟絫f(x)锟紻锟斤拷锟絇(gu锟斤拷n)锟斤拷(a锟斤拷b)锟斤拷锟侥岋拷(du锟斤拷)锟絈

锟斤拷锟斤拷4.锟斤拷锟斤拷(sh锟斤拷)锟斤拷偶锟皆ｏ拷

锟斤拷锟斤拷(1)锟斤拷(du锟斤拷)锟节岋拷锟斤拷R锟较碉拷锟芥函锟斤拷(sh锟斤拷)锟斤拷f(0)=0

锟斤拷锟斤拷(2)锟斤拷(du锟斤拷)锟节猴拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)锟斤拷锟芥函锟斤拷(sh锟斤拷)锟絔锟斤拷偶锟轿凤拷锟�(xi锟斤拷ng)锟斤拷偶锟斤拷锟斤拷(sh锟斤拷)锟絔锟斤拷锟斤拷畏锟斤拷(xi锟斤拷ng)

锟斤拷锟斤拷(3)锟斤拷偶锟斤拷锟斤拷锟矫诧拷锟斤拷锟斤拷一锟斤拷锟斤拷锟斤拷锟絰锟斤拷锟斤拷锟�

锟斤拷锟斤拷5.锟斤拷(sh锟斤拷)锟叫憋拷锟斤拷(qi锟斤拷ng)锟斤拷锟缴ｏ拷

锟斤拷锟斤拷1.锟饺差數(sh锟斤拷)锟斤拷锟叫ｏ拷S锟斤拷=na锟斤拷锟斤拷锟斤拷锟斤拷S 13 =13a 7

锟斤拷锟斤拷2.锟饺差數(sh锟斤拷)锟斤拷锟叫ｏ拷S(n)锟斤拷S(2n)-S(n)锟斤拷S(3n)-S(2n)锟缴等诧拷

锟斤拷锟斤拷3.锟饺比旓拷(sh锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷2锟叫革拷锟�(xi锟斤拷ng)锟节癸拷锟饺诧拷锟斤拷負(f锟斤拷)一锟絩(sh锟斤拷)锟缴等憋拷锟斤拷锟斤拷q=-1锟絩(sh锟斤拷)锟斤拷未锟截筹拷锟斤拷

锟斤拷锟斤拷4.锟饺比旓拷(sh锟斤拷)锟叫憋拷锟斤拷(qi锟斤拷ng)锟斤拷式锟斤拷S(n+m)=S(m)+q2mS(n)锟斤拷锟斤拷迅锟斤拷锟斤拷q

锟斤拷锟斤拷6.锟斤拷(sh锟斤拷)锟叫的終锟絆锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷(锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟�)锟斤拷

锟斤拷锟斤拷锟斤拷锟饺斤拷B锟斤拷式锟斤拷锟斤拷(du锟斤拷)锟斤拷a n+1 =pa n +q锟斤拷a1锟斤拷知锟斤拷锟斤拷么锟斤拷锟斤拷锟斤拷x=q/(1-p)锟斤拷锟絫锟斤拷(sh锟斤拷)锟斤拷通锟�(xi锟斤拷ng)锟斤拷式锟斤拷an=(a1-x)p2(n-1)+x锟斤拷锟紷锟斤拷一锟紸锟斤拷锟斤拷锟斤拷锟斤拷锟教碉拷锟絓(y锟斤拷n)锟斤拷锟斤拷锟斤拷锟紸锟斤拷锟絚(di锟斤拷n)锟介煩锟斤拷锟揭诧拷锟斤拷锟斤拷锟斤拷锟斤拷锟皆诧拷贅锟斤拷锟斤拷希锟斤拷同锟絎(xu锟斤拷)锟斤拷锟斤拷記锟斤拷锟斤拷锟斤拷式锟斤拷锟斤拷(d锟斤拷ng)然锟紷锟絅锟斤拷偷臄锟�(sh锟斤拷)锟叫匡拷锟皆橈拷(g锟斤拷u)锟斤拷(锟斤拷邊同锟絩(sh锟斤拷)锟接旓拷(sh锟斤拷))

锟斤拷锟斤拷7.锟斤拷锟斤拷(sh锟斤拷)詳锟斤拷锟絘(b锟斤拷)锟戒：

锟斤拷锟斤拷(1)锟斤拷(f锟斤拷)锟较猴拷锟斤拷(sh锟斤拷)锟斤拷偶锟皆ｏ拷锟斤拷(n锟斤拷i)偶锟絫偶锟斤拷锟斤拷(n锟斤拷i)锟斤拷同锟斤拷

锟斤拷锟斤拷(2)锟斤拷(f锟斤拷)锟较猴拷锟斤拷(sh锟斤拷)锟斤拷锟絳(di锟斤拷o)锟皆ｏ拷同锟斤拷锟斤拷锟絧

锟斤拷锟斤拷(3)锟斤拷锟絚(di锟斤拷n)知锟絉(sh锟斤拷)锟絇(gu锟斤拷n)锟斤拷锟斤拷锟轿猴拷锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟铰沒锟叫讹拷锟斤拷锟斤拷知锟斤拷锟斤拷锟轿猴拷锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟戒實(sh锟斤拷)锟斤拷锟斤拷锟侥岋拷(du锟斤拷)锟絈锟紻锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷(g锟斤拷)锟斤拷(du锟斤拷)锟絈锟斤拷锟侥ｏ拷锟襟法烇拷锟斤拷A锟斤拷(d锟斤拷o)锟斤拷(d锟斤拷o)锟斤拷(sh锟斤拷)锟斤拷0锟斤拷锟斤拷x锟斤拷锟斤拷锟斤拷锟侥橫锟斤拷锟斤拷(bi锟斤拷o)锟斤拷锟絭锟斤拷锟斤拷(bi锟斤拷o)锟斤拷锟斤拷锟斤拷x锟斤拷锟斤拷原锟斤拷锟斤拷(sh锟斤拷)锟界定锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷唯一一锟絣锟絕該锟斤拷锟侥碉拷直锟斤拷锟絚锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷8.锟斤拷锟矫旓拷(sh锟斤拷)锟斤拷bn=n×(22n)锟斤拷锟絊n=(n-1)×(22(n+1))+2記锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷前锟斤拷p去一锟斤拷(g锟斤拷)1锟斤拷锟斤拷锟斤拷锟揭伙拷锟�(g锟斤拷)锟斤拷锟斤拷锟斤拷锟絯锟斤拷一锟斤拷(g锟斤拷)2

锟斤拷锟斤拷9.锟絤锟斤拷锟节橈拷(bi锟斤拷o)锟斤拷(zh锟斤拷n)锟斤拷锟斤拷(锟斤拷锟絚(di锟斤拷n)锟斤拷x锟絊)锟斤拷锟斤拷(qi锟斤拷ng)锟斤拷式

锟斤拷锟斤拷k锟紼=-{(b2)xo锟斤拷/{(a2)yo锟斤拷k锟絧={(b2)xo锟斤拷/{(a2)yo锟斤拷k锟斤拷=p/yo

锟斤拷锟斤拷注锟斤拷(xo锟斤拷yo)锟斤拷锟斤拷直锟斤拷锟絕锟紸锟紽锟斤拷锟斤拷锟斤拷锟截段碉拷锟斤拷锟絚(di锟斤拷n)锟斤拷

锟斤拷锟斤拷10.锟斤拷(qi锟斤拷ng)锟斤拷锟斤拷锟絔一锟斤拷(g锟斤拷)锟斤拷直锟斤拷锟斤拷直锟斤拷平锟叫的必氾拷锟斤拷

锟斤拷锟斤拷锟斤拷知直锟斤拷L1锟斤拷a1x+b1y+c1=0 直锟斤拷L2锟斤拷a2x+b2y+c2=0

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷直锟斤拷(锟斤拷要锟絣锟斤拷)a1a2+b1b2=0;

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷平锟叫ｏ拷(锟斤拷要锟絣锟斤拷)a1b2=a2b1锟斤拷a1c2≠a2c1[锟紷锟斤拷(g锟斤拷)锟絣锟斤拷锟斤拷锟剿凤拷止锟斤拷直锟斤拷锟截猴拷)

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锟組锟斤拷"锟竭匡拷锟絎(w锟斤拷ng)"微锟脚癸拷锟斤拷號(h锟斤拷o)