1 . 锟絤锟矫條锟斤拷

[直锟斤拷锟絕锟斤拷锟絚]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锟饺凤拷(指锟斤拷锟角斤拷锟絚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(锟斤拷锟絚锟斤拷锟斤拷锟截撅拷锟斤拷锟斤拷锟絃锟斤拷锟斤拷)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

2 . 锟斤拷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)

(1)锟斤拷f(x)=-f(x+k)锟斤拷锟絫T=2k;(2)锟斤拷f(x)=m/(x+k)(m锟斤拷锟斤拷0)锟斤拷锟絫T=2k;(3)锟斤拷f(x)=f(x+k)+f(x-k)锟斤拷锟絫T=6k锟斤拷

注锟斤拷锟絚锟斤拷a.锟斤拷锟节猴拷锟斤拷锟斤拷锟斤拷锟节必無锟斤拷b.锟斤拷锟节猴拷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：锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷c.锟斤拷锟节猴拷锟斤拷锟斤拷锟斤拷锟节猴拷锟斤拷未锟斤拷锟斤拷锟斤拷锟节猴拷锟斤拷锟斤拷锟界：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�锟斤拷

3 . 锟絇锟节岋拷锟絈锟斤拷锟絵(锟給锟斤拷锟剿搞不锟斤拷锟侥嗭拷锟絵)锟斤拷锟結锟斤拷锟斤拷

(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�锟斤拷锟斤拷锟絈锟絊锟斤拷x=(a+b)/2(2)锟斤拷锟斤拷y=f(a+x)锟絚y=f(b-x)锟侥圖锟斤拷锟絇锟斤拷x=(b-a)/2锟斤拷锟絈;(3)锟斤拷f(a+x)+f(a-x)=2b锟斤拷锟絫f(x)锟紻锟斤拷锟絇锟斤拷(a锟斤拷b)锟斤拷锟侥岋拷锟絈

4 . 锟斤拷锟斤拷锟斤拷偶锟斤拷

(1)锟斤拷锟节岋拷锟斤拷R锟较碉拷锟芥函锟斤拷锟斤拷f(0)=0;(2)锟斤拷锟节猴拷锟斤拷锟斤拷锟斤拷锟斤拷锟芥函锟斤拷锟絔锟斤拷偶锟轿凤拷锟�锟斤拷偶锟斤拷锟斤拷锟絔锟斤拷锟斤拷畏锟斤拷(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�

5 . 锟斤拷锟叫憋拷锟斤拷锟斤拷锟斤拷

(1)锟饺差數锟斤拷锟叫ｏ拷S锟斤拷=na锟斤拷锟斤拷锟斤拷锟斤拷S13=13a7(13锟斤拷7锟斤拷锟铰角橈拷);(2)锟饺差數锟斤拷锟叫ｏ拷S(n)锟斤拷S(2n)-S(n)锟斤拷S(3n)-S(2n)锟缴等诧拷(3)锟饺比旓拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷2锟叫革拷锟斤拷诠锟斤拷炔锟斤拷锟截撘伙拷r锟缴等憋拷锟斤拷锟斤拷q=-1锟絩锟斤拷未锟截筹拷锟斤拷(4)锟饺比旓拷锟叫憋拷锟斤拷锟斤拷式锟斤拷S(n+m)=S(m)+q²mS(n)锟斤拷锟斤拷迅锟斤拷锟斤拷q

6 . 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

锟斤拷锟饺斤拷B锟斤拷式锟斤拷锟斤拷锟斤拷an+1=pan+q(n+1锟斤拷锟铰角橈拷锟斤拷n锟斤拷锟铰角橈拷)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)锟斤拷锟絫锟斤拷锟斤拷通項癸拷式锟斤拷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锟斤拷锟斤拷

锟斤拷锟紸锟斤拷锟絚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锟斤拷锟斤拷記锟斤拷锟斤拷锟斤拷式锟斤拷锟斤拷然锟紷锟絅锟斤拷偷臄锟斤拷锌锟斤拷詷锟斤拷锟�(锟斤拷邊同锟絩锟接旓拷)

7 . 锟斤拷锟斤拷詳锟斤拷锟絘锟斤拷

1锟斤拷锟酵合猴拷锟斤拷锟斤拷偶锟皆ｏ拷锟斤拷偶锟絫偶锟斤拷锟斤拷锟斤拷同锟斤拷2锟斤拷锟酵合猴拷锟斤拷锟斤拷锟絳锟皆ｏ拷同锟斤拷锟斤拷锟絧3锟斤拷锟斤拷锟絚知锟絉锟絇锟斤拷锟斤拷锟轿猴拷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锟斤拷锟斤拷锟戒實锟斤拷锟斤拷锟侥岋拷锟絈锟紻锟斤拷锟斤拷

锟斤拷锟斤拷一锟斤拷锟斤拷锟絈锟斤拷锟侥ｏ拷锟襟法烇拷锟斤拷A锟斤拷锟襟導旓拷锟斤拷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锟斤拷锟絭锟斤拷锟剿匡拷锟斤拷锟斤拷x锟斤拷锟斤拷原锟斤拷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

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

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

9 . 锟絤锟斤拷锟节標準凤拷锟斤拷(锟斤拷锟絚锟斤拷x锟絊)锟斤拷锟斤拷锟斤拷式

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

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锟斤拷

10 . 锟斤拷锟斤拷锟斤拷锟絔一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[锟紷锟斤拷锟絣锟斤拷锟斤拷锟剿凤拷止锟斤拷直锟斤拷锟截猴拷)

注锟斤拷锟斤拷锟较兩癸拷式锟斤拷锟斤拷锟斤拷斜锟斤拷锟角凤拷锟斤拷诘锟斤拷闊�锟斤拷直锟接必氾拷!

11 . 锟斤拷锟斤拷锟叫的斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟揭讹拷知锟斤拷锟斤拷锟斤拷锟芥看锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絊n=1/(1×3)+1/(2×4)+1/(3×5)+…+1/[n(n+2)]=1/2[1+1/2-1/(n+1)-1/(n+2)]

注锟斤拷锟斤拷锟斤拷锟接憋拷锟斤拷锟斤拷項ｏ拷锟斤拷锟阶冿拷锟�锟斤拷尾锟斤拷項★拷锟皆硷拷锟斤拷式锟接岋拷锟节草稿紙锟斤拷锟斤拷锟角樣匡拷锟斤拷锟斤拷锟斤拷锟斤拷锟剿�锟皆硷拷锟斤拷锟斤拷!

12 . 锟斤拷锟斤拷锟斤拷锟斤拷e锟斤拷式

S=1/2锟絆mq-np锟絆锟斤拷锟斤拷锟斤拷锟斤拷AB=(m锟斤拷n)锟斤拷锟斤拷锟斤拷BC=(p锟斤拷q)

注锟斤拷锟紷锟斤拷锟斤拷式锟斤拷锟皆斤拷Q锟斤拷知锟斤拷锟斤拷锟斤拷锟斤拷锟絚锟斤拷锟斤拷锟斤拷锟斤拷e锟侥嗭拷锟絵

13 . 锟斤拷知锟斤拷锟斤拷?锟斤拷锟絞锟斤拷锟絯锟阶猴拷锟叫ｏ拷锟斤拷锟斤拷锟斤拷锟絵锟斤拷锟絜

(1)锟斤拷锟絞锟叫诧拷同锟斤拷锟絚锟絖锟斤拷一锟斤拷平锟斤拷(2)锟斤拷直同一直锟斤拷锟侥冿拷直锟斤拷平锟斤拷(3)锟缴組锟斤拷邊锟街別锟斤拷鹊锟斤拷锟竭咃拷锟斤拷锟狡斤拷锟斤拷锟竭咃拷锟�(4)锟斤拷锟揭伙拷l直锟斤拷锟絚平锟斤拷葻o锟斤拷锟絣直锟斤拷锟斤拷直锟斤拷锟絫直锟斤拷锟斤拷直平锟斤拷(5)锟叫兩傦拷锟芥互锟斤拷平锟叫ｏ拷锟斤拷锟斤拷锟斤拷娑硷拷锟狡斤拷锟斤拷锟竭咃拷蔚膸缀锟斤拷w锟斤拷锟斤拷锟斤拷(6)锟斤拷一锟斤拷锟斤拷锟角讹拷邊锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷娑硷拷锟斤拷锟斤拷锟斤拷蔚膸缀锟斤拷w锟斤拷锟斤拷锟斤拷锟紽

注锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絤锟矫★拷

14 . 一锟斤拷小知锟絉锟絚

锟斤拷锟斤拷锟斤拷锟絃锟斤拷锟斤拷鹊锟斤拷锟斤拷F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紽锟斤拷

15 . 锟斤拷f(x)=锟絆x-1锟絆+锟絆x-2锟絆+锟絆x-3锟絆+…+锟絆x-n锟絆(n锟斤拷锟斤拷锟斤拷锟斤拷)锟斤拷锟斤拷小值

锟金案為：锟斤拷n锟斤拷锟芥數锟斤拷锟斤拷小值锟斤拷(n²-1)/4锟斤拷锟斤拷x=(n+1)/2锟絩取锟斤拷;

锟斤拷n锟斤拷偶锟斤拷锟絩锟斤拷锟斤拷小值锟斤拷n²/4锟斤拷锟斤拷x=n/2锟斤拷n/2+1锟絩取锟斤拷锟斤拷

16 . √锟斤拷(a²+b²)锟斤拷/2≥(a+b)/2≥√ab≥2ab/(a+b)(a锟斤拷b锟斤拷锟斤拷锟斤拷锟斤拷锟角統一锟斤拷锟絰锟斤拷)

17 . 锟紼锟紸锟叫斤拷锟絚锟斤拷锟斤拷锟斤拷锟斤拷e锟斤拷式

S=b²tan(A/2)锟斤拷锟絧锟斤拷锟斤拷锟叫ｏ拷S=b²/tan(A/2)

锟絝锟斤拷锟斤拷锟絤锟斤拷锟节斤拷锟絚锟斤拷x锟絊锟斤拷锟揭標準的圓锟紽锟斤拷锟斤拷锟斤拷A锟斤拷山锟斤拷霃斤拷A锟斤拷锟斤拷

18 . 锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟絞锟斤拷锟斤拷锟斤拷锟斤拷式锟斤拷Q锟斤拷锟斤拷锟絵目锟斤拷cosA=|{锟斤拷锟斤拷a.锟斤拷锟斤拷b锟斤拷/[锟斤拷锟斤拷a锟斤拷模×锟斤拷锟斤拷b锟斤拷模](1)A锟介線锟斤拷锟紸锟斤拷(2)A锟介線锟斤拷A锟斤拷(锟斤拷锟角癸拷式锟斤拷cos锟絈锟斤拷sin)(3)A锟斤拷锟斤拷锟斤拷A锟斤拷注锟斤拷锟斤拷锟较角凤拷锟斤拷锟斤拷锟斤拷[0锟斤拷锟斤拷/2]锟斤拷

19 . 锟斤拷锟斤拷锟斤拷式

1²+2²+3²+…+n²=1/6(n)(n+1)(2n+1);1²3+2²3+3²3+…+n²3=1/4(n²)(n+1)²

20 . 锟斤拷锟斤拷锟叫撅拷锟斤拷锟斤拷記锟斤拷锟斤拷锟斤拷

锟斤拷锟缴岋拷锟絈锟斤拷式锟斤拷锟絈一锟斤拷x锟斤拷锟絈一锟斤拷y

锟絜锟斤拷锟絝锟斤拷锟斤拷锟斤拷锟斤拷y²=2px锟斤拷锟皆岋拷锟斤拷y×y=px+px锟劫帮拷(xo锟斤拷yo)锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷锟矫ｏ拷y×yo=pxo+px

21 . 锟斤拷锟斤拷锟斤拷锟斤拷

(a+b+c)²n锟斤拷展锟絖式[锟较诧拷之锟斤拷]锟斤拷項旓拷锟介：Cn+22锟斤拷n+2锟斤拷锟斤拷锟斤拷2锟斤拷锟斤拷

22 . 锟紻锟斤拷思锟斤拷

锟叫撅拷锟絃l=√(d²-r²)d锟斤拷示锟紸锟斤拷一锟絚锟斤拷锟紸锟侥得撅拷锟絰锟斤拷r锟斤拷A锟诫徑锟斤拷锟斤拷d锟斤拷小锟斤拷A锟侥碉拷直锟斤拷锟侥撅拷锟絰锟斤拷

23 . 锟斤拷锟斤拷y²=2px

锟絕锟斤拷锟絚锟侥伙拷锟洁垂直锟侥冿拷锟斤拷AB锟斤拷CD锟斤拷锟斤拷锟斤拷锟侥猴拷锟斤拷小锟斤拷8p锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟紺锟斤拷锟斤拷锟斤拷锟斤拷y²=2px锟斤拷锟絆锟絕锟斤拷锟絚锟斤拷锟揭傾斜锟角烇拷A锟斤拷么锟斤拷锟絃锟缴憋拷示锟斤拷2p/锟斤拷(sinA)²锟斤拷锟斤拷锟斤拷锟斤拷锟絚之锟斤拷直锟斤拷锟斤拷锟絃锟斤拷2p/[(cosA)²]锟斤拷锟斤拷锟斤拷锟斤拷贀锟斤拷锟斤拷锟街�锟絉锟斤拷知锟斤拷(锟絵目锟斤拷锟斤拷思锟斤拷锟斤拷锟斤拷AB锟絕锟斤拷锟絚锟斤拷CD锟絕锟斤拷锟絚锟斤拷锟斤拷AB锟斤拷直锟斤拷CD)

24 . 锟絇锟斤拷一锟斤拷锟斤拷要锟絕锟斤拷值锟斤拷锟斤拷式锟侥斤拷B锟斤拷锟斤拷

锟絆|a|-|b|锟絆≤锟絆a±b锟絆≤锟絆a锟絆+锟絆b锟絆

25 . 锟絇锟节斤拷Q锟紺锟斤拷锟斤拷ln锟侥诧拷锟斤拷式锟斤拷一锟絅思路

锟絜锟斤拷锟絝锟斤拷锟斤拷锟紺锟斤拷1+1/2+1/3+…+1/n>ln(n+1)

锟斤拷锟斤拷邊锟斤拷锟斤拷锟斤拷1/n锟斤拷锟�锟斤拷锟斤拷邊锟斤拷锟斤拷锟斤拷Sn锟斤拷

锟解：锟斤拷an=1/n锟斤拷锟斤拷Sn=ln(n+1)锟斤拷锟絫bn=ln(n+1)-lnn锟斤拷锟斤拷么只锟斤拷锟紺an>bn锟斤拷锟缴ｏ拷锟斤拷锟斤拷锟斤拷锟絜锟斤拷知锟絉锟斤拷锟斤拷y=1/x锟侥圖锟斤拷an=1×1/n=锟斤拷锟斤拷锟斤拷e>锟斤拷锟斤拷锟斤拷锟斤拷e=bn锟斤拷锟斤拷然前锟斤拷要锟紺锟斤拷1>ln2锟斤拷

注锟斤拷锟紿锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷童鞋锟斤拷锟斤拷!!锟斤拷锟解對锟斤拷锟紷锟絅锟斤拷锟斤拷锟斤拷锟斤拷锟狡廣锟斤拷锟斤拷锟角帮拷锟斤拷邊锟斤拷锟斤拷邊锟斤拷锟斤拷锟角旓拷锟斤拷锟斤拷停锟斤拷C锟斤拷e锟斤拷小锟斤拷锟斤拷锟斤拷锟絝锟斤拷锟斤拷前锟斤拷锟角猴拷ln锟斤拷

26 . 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷式

锟斤拷锟斤拷a锟斤拷锟斤拷锟斤拷b锟较碉拷锟斤拷影锟角ｏ拷锟斤拷锟斤拷锟斤拷a×锟斤拷锟斤拷b锟侥旓拷锟斤拷锟絜锟斤拷/[锟斤拷锟斤拷b锟斤拷模]锟斤拷記锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷投影锟斤拷锟斤拷锟侥傦拷锟斤拷模

27 . 锟絝锟斤拷一锟斤拷锟斤拷锟絜锟絚

锟斤拷f(x+a)[a锟斤拷锟斤拷]锟斤拷锟芥函锟斤拷锟斤拷锟斤拷么锟矫碉拷锟侥結論锟斤拷f(x+a)=-f(-x+a)锟斤拷锟斤拷式锟斤拷邊锟斤拷锟斤拷-f(-x-a)锟斤拷同锟斤拷锟斤拷锟絝(x+a)锟斤拷偶锟斤拷锟斤拷锟斤拷锟缴碉拷f(x+a)=f(-x+a) 锟斤拷記

28 . 锟絰锟斤拷锟绞憋拷锟斤拷锟斤拷式

e=sinA/(sinM+sinN)

注锟斤拷P锟斤拷E锟紸锟斤拷一锟絚锟斤拷锟斤拷锟斤拷A锟斤拷锟紽1PF2锟斤拷锟斤拷锟斤拷锟角烇拷M锟斤拷N

29 . 锟紼锟紸锟侥咃拷锟斤拷锟斤拷锟斤拷也锟斤拷一锟斤拷锟杰好的東锟斤拷锟斤拷锟斤拷锟斤拷锟皆斤拷Q一些锟斤拷值锟斤拷锟絵锟斤拷

锟斤拷锟斤拷x²/4+y²=1锟斤拷z=x+y锟斤拷锟斤拷值锟斤拷锟解：锟斤拷x=2cosay=sina锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟叫界即锟斤拷锟斤拷锟斤拷锟斤拷去=0锟斤拷知锟斤拷锟斤拷锟斤拷俦锟�!

30 . 锟紿锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷童鞋锟斤拷锟斤拷锟侥憋拷锟斤拷锟斤拷式

锟酵差化锟絜sinθ+sinφ=2sin[(θ+φ)/2]cos[(θ-φ)/2]sinθ-sinφ=2cos[(θ+φ)/2]sin[(θ-φ)/2]cosθ+cosφ=2cos[(θ+φ)/2]cos[(θ-φ)/2]cosθ-cosφ=-2sin[(θ+φ)/2]sin[(θ-φ)/2]

锟絜锟斤拷锟酵诧拷sinαsinβ=[cos(α-β)-cos(α+β)]/2cosαcosβ=[cos(α+β)+cos(α-β)]/2sinαcosβ=[sin(α+β)+sin(α-β)]/2cosαsinβ=[sin(α+β)-sin(α-β)]/2

31 . 锟斤拷锟斤拷锟斤拷锟斤拷

直锟絕锟紻锟斤拷锟斤拷e锟斤拷原锟紻锟斤拷√2/4锟斤拷锟斤拷

32 . 锟斤拷锟斤拷锟轿达拷锟侥憋拷锟斤拷锟斤拷锟斤拷

(1)锟斤拷锟斤拷OH=锟斤拷锟斤拷OA+锟斤拷锟斤拷OB+锟斤拷锟斤拷OC(O锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷H锟介垂锟斤拷)

(2)锟斤拷锟斤拷锟斤拷锟轿碉拷锟斤拷锟斤拷锟斤拷c锟斤拷锟节猴拷锟斤拷y=1/x锟侥圖锟斤拷锟斤拷锟斤拷锟絫锟斤拷锟侥达拷锟斤拷也锟斤拷锟紷锟斤拷锟斤拷锟斤拷锟紻锟斤拷锟斤拷锟斤拷

33 . 锟絊锟絊锟斤拷锟结定锟斤拷(锟斤拷锟角猴拷锟斤拷要(锟紿锟斤拷锟绞橈拷))

锟斤拷锟斤拷锟斤拷锟轿冿拷(锟斤拷邊锟斤拷锟斤拷)锟斤拷一锟絚锟斤拷锟斤拷邊锟侥撅拷锟絰之锟酵為定值锟斤拷锟紷锟斤拷值锟斤拷锟斤拷該锟斤拷锟斤拷锟轿的高★拷

34 . 锟斤拷锟斤拷思路

锟斤拷锟斤拷锟斤拷F锟缴革拷之锟絜x1x2=m锟斤拷锟缴革拷之锟斤拷x1+x2=n

锟揭傦拷锟斤拷锟斤拷锟轿筹拷一锟絅思路锟斤拷锟角撅拷锟角凤拷锟斤拷去锟斤拷锟斤拷一锟斤拷锟斤拷锟轿猴拷锟斤拷锟斤拷锟斤拷锟矫★拷锟斤拷锟节碉拷锟斤拷0锟斤拷锟斤拷锟皆得碉拷m锟斤拷n锟斤拷锟斤拷锟斤拷

35 . 锟斤拷锟矫結論

锟絕(2p锟斤拷0)锟斤拷直锟斤拷锟斤拷锟斤拷锟斤線y²=2px锟斤拷A锟斤拷B锟斤拷锟絚锟斤拷

O锟斤拷原锟絚锟斤拷锟紹锟斤拷AO.BO锟斤拷锟斤拷锟叫斤拷AOB=90锟斤拷

36 . 锟斤拷锟斤拷锟斤拷式

ln(x+1)≤x(x>-1)該式锟斤拷锟斤拷效锟斤拷Q锟斤拷锟斤拷式锟斤拷锟紺锟斤拷锟斤拷锟絵锟斤拷

锟絜锟斤拷锟絝锟斤拷锟斤拷ln(1/(2²)+1)+ln(1/(3²)+1)+…+ln(1/(n²)+1)<1(n≥2)锟紺锟斤拷锟斤拷锟铰ｏ拷锟斤拷x=1/(n²)锟斤拷锟斤拷锟斤拷ln(x+1)≤x锟斤拷锟斤拷锟斤拷锟桔猴拷锟斤拷邊锟劫放縮锟矫ｏ拷锟斤拷锟�<1-1/n<1锟紺锟斤拷!

37 . 锟斤拷锟斤拷y=(sinx)/x锟斤拷偶锟斤拷锟斤拷

锟斤拷(0锟斤拷锟斤拷)锟斤拷锟斤拷锟斤拷锟絳锟絝锟絧锟斤拷(-锟斤拷锟斤拷0)锟较嗭拷锟絳锟絝锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絴锟斤拷锟皆憋拷锟絕锟斤拷小锟斤拷

38 . 锟斤拷锟斤拷

y=(lnx)/x锟斤拷(0锟斤拷e)锟较嗭拷锟絳锟絝锟斤拷锟斤拷锟斤拷(e锟斤拷+锟給锟紽)锟较嗭拷锟絳锟絝锟絧锟斤拷

锟斤拷锟斤拷y=x²(1/x)锟絚該锟斤拷锟斤拷锟侥嗭拷锟絳锟斤拷一锟铰★拷

39 . 锟阶傦拷锟斤拷锟絎锟斤拷锟絜锟絚

(1)f`(x)<0锟角猴拷锟斤拷锟节讹拷锟絰锟斤拷葐锟斤拷{锟絝锟絧锟侥筹拷植锟斤拷锟揭�锟絣锟斤拷(2)锟叫撅拷锟斤拷锟斤拷锟斤拷偶锟皆時锟斤拷锟斤拷锟斤拷锟斤拷锟絖始锟斤拷也锟斤拷锟斤拷锟斤拷要锟斤拷一锟斤拷锟斤拷锟斤拷锟絔锟斤拷锟絰锟斤拷锟角凤拷锟絇锟斤拷原锟絚锟斤拷锟絈(3)锟斤拷锟斤拷式锟斤拷锟絓锟斤拷锟絕锟斤拷锟叫ｏ拷千锟絝要锟斤拷锟絔"="號锟角凤拷取锟斤拷(4)锟叫撅拷锟斤拷锟叫嗭拷锟絵锟斤拷锟斤拷锟絔锟斤拷锟�锟斤拷锟斤拷锟斤拷锟絝锟叫時锟斤拷一項诧拷锟斤拷锟斤拷锟斤拷通項癸拷式锟斤拷锟斤拷锟皆戯拷锟斤拷锟絆锟斤拷注锟解：锟斤拷锟叫嗭拷锟絵一锟斤拷要锟斤拷锟絔锟角凤拷锟斤拷要锟斤拷锟�!

40 . 锟斤拷锟接嬶拷锟斤拷锟斤拷锟斤拷宀斤拷锟�

(1)锟接碉拷計锟斤拷锟斤拷(2)锟叫硷拷锟斤拷锟絵(锟结倡锟斤拷锟絵锟斤拷锟斤拷锟斤拷锟絵锟斤拷)锟斤拷要知锟斤拷锟絔锟叫匡拷锟斤拷锟斤拷}目锟斤拷锟斤拷锟斤拷锟斤拷俣锟斤拷]锟斤拷(3)锟斤拷記锟斤拷锟矫旓拷锟斤拷锟斤拷锟斤拷锟斤拷一些锟斤拷锟姐技(4)锟接忥拷锟斤拷锟姐、锟斤拷锟斤拷锟斤拷锟斤拷(5)锟絲锟�

41 . 一锟斤拷锟斤拷锟斤拷墓锟绞�

锟斤拷知锟斤拷锟斤拷锟斤拷锟斤拷AB=a锟斤拷AC=b锟斤拷O锟斤拷锟斤拷锟斤拷锟轿碉拷锟斤拷锟斤拷锟斤拷锟絫锟斤拷锟斤拷AO×锟斤拷锟斤拷BC(锟斤拷锟斤拷锟斤拷锟絜)=(1/2)[b²-a²]锟紺锟斤拷锟斤拷锟絕O锟斤拷BC锟斤拷锟斤拷锟斤拷锟紻锟斤拷锟斤拷锟斤拷知邊锟斤拷

42 . 锟斤拷锟斤拷

锟劫猴拷锟斤拷锟斤拷锟絳锟皆的猴拷锟絰锟斤拷锟斤拷锟斤拷锟酵�锟絎锟斤拷知锟斤拷锟斤拷锟斤拷锟斤拷锟节區(q锟斤拷)锟絞D锟较嗭拷锟絳锟斤拷锟絫锟斤拷锟斤拷值锟絊锟斤拷锟斤拷變锟斤拷锟斤拷锟斤拷锟斤拷(锟絧小)锟斤拷锟斤拷锟斤拷(锟絧小)锟斤拷锟斤拷锟斤拷些锟斤拷思锟斤拷锟斤拷锟斤拷些锟斤拷還锟斤拷锟角猴拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟紻锟较嗭拷锟絳锟斤拷锟絫锟斤拷锟斤拷锟斤拷锟紹锟絤(x锟斤拷)(锟街段猴拷锟斤拷锟斤拷锟斤拷锟絜論)锟紷也锟絝锟斤拷锟剿烇拷什么锟斤拷锟斤拷锟絝y=tanx锟节讹拷锟絰锟斤拷葐锟斤拷{锟絝锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷膱D锟今被無锟紽锟斤拷锟絣锟絬锟斤拷锟斤拷锟斤拷住锟斤拷锟絈锟斤拷锟斤拷之锟斤拷锟斤拷锟紹锟絤(x锟斤拷).還锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟紻锟较嗭拷锟絳锟斤拷锟絫锟斤拷锟斤拷锟斤拷D锟斤拷y锟絚x一一锟斤拷锟斤拷.锟紷锟斤拷锟斤拷锟斤拷锟矫侊拷锟斤拷一些锟斤拷锟斤拷.锟斤拷锟斤拷锟斤拷锟接诧拷锟絜锟斤拷

锟节猴拷锟斤拷锟斤拷锟斤拷锟皆ｏ拷锟紷锟斤拷锟斤拷要锟斤拷锟結一些锟斤拷锟斤拷锟斤拷锟斤拷式锟斤拷要锟斤拷锟絖锟斤拷锟斤拷锟斤拷锟絆f(x)锟斤拷R锟较的猴拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷x∈R(1)f(a±x)=f(b±x)T=(b-a)(锟接絕锟斤拷值锟斤拷锟斤拷同)(2)f(a±x)=-f(b±x)T=2(b-a)(3)f(x-a)+f(x+a)=f(x)T=6a(4)锟絆T≠0锟斤拷锟斤拷f(x+T)=M[f(x)]锟斤拷锟斤拷M(x)锟組锟斤拷M[M(x)]=x,锟斤拷M(x)≠x锟絫锟斤拷锟斤拷锟斤拷锟斤拷锟节烇拷2

43 . 锟斤拷偶锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷茝V

(1)锟斤拷锟节猴拷锟斤拷f(x)锟斤拷锟斤拷锟斤拷锟节筹拷锟斤拷a锟斤拷使锟斤拷f(a-x)=f(a+x)锟斤拷锟絫锟絈f(x)锟斤拷V锟絰(锟斤拷)锟斤拷偶锟斤拷锟斤拷锟斤拷锟揭�锟斤拷袃蓚锟斤拷喈愶拷锟斤拷锟絘锟斤拷b锟組锟斤拷r锟斤拷f(x)锟斤拷锟斤拷锟节猴拷锟斤拷T=2(b-a)

(2)锟斤拷f(a-x)=-f(a+x)锟斤拷锟絫f(x)锟角廣锟絰(锟斤拷)锟斤拷锟芥函锟斤拷锟斤拷锟斤拷锟叫兩傦拷锟洁異锟斤拷锟斤拷a锟斤拷b锟組锟斤拷r锟斤拷f(x)锟斤拷锟斤拷锟节猴拷锟斤拷T=2(b-a)

(3)锟叫兩傦拷锟斤拷锟斤拷a锟斤拷b锟組锟斤拷V锟絰锟斤拷偶锟斤拷锟斤拷锟侥凤拷锟斤拷式锟絩锟斤拷锟酵稱f(x)锟角廣锟絰(锟斤拷)锟酵碉拷锟斤拷锟斤拷偶锟斤拷锟斤拷.锟斤拷锟斤拷f(x)锟角廣锟絰(锟斤拷)锟斤拷偶锟斤拷锟斤拷锟斤拷锟斤拷么锟斤拷f锟斤拷[a+b/2锟斤拷∞)锟较烇拷锟斤拷锟斤拷锟斤拷锟絩锟斤拷锟斤拷f(x1)

44 . 锟斤拷锟斤拷锟斤拷锟絈锟斤拷

(1)锟斤拷f(x)锟組锟斤拷f(a+x)+f(b-x)=c锟絫锟斤拷锟斤拷锟絇锟斤拷(a+b/2锟斤拷c/2)锟斤拷锟斤拷锟侥岋拷锟絈(2)锟斤拷f(x)锟組锟斤拷f(a+x)=f(b-x)锟絫锟斤拷锟斤拷锟絇锟斤拷直锟斤拷x=a+b/2锟斤拷锟絊锟斤拷锟絈

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟教ｏ拷锟斤拷f(x)锟紹锟絤(x锟斤拷)锟斤拷锟斤拷{(1)锟斤拷f(xy)=f(x)+f(y)(x>0,y>0),锟絫f(x)=锟絊ax(2)锟斤拷f(xy)=f(x)f(y)(x>0,y>0),锟絫f(x)=x²u(u锟缴筹拷值锟給锟斤拷)(3)f(x+y)=f(x)f(y)锟絫f(x)=a²x(4)锟斤拷f(x+y)=f(x)+f(y)+kxy,锟絫f(x)=ax2+bx(5)锟斤拷f(x+y)+f(x-y)=2f(x),锟絫f(x)=ax+b锟截別锟斤拷锟斤拷f(x)+f(y)=f(x+y)锟斤拷锟絫f(x)=kx

45 . 锟絚锟斤拷锟斤拷锟斤拷锟斤拷锟絇锟侥讹拷锟斤拷锟斤拷Y論锟叫學锟斤拷锟絎平锟斤拷缀锟斤拷锟斤拷锟斤拷锟侥圖锟轿撅拷锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷锟叫讹拷锟斤拷(锟斤拷锟皆硷拷取锟斤拷锟斤拷锟斤拷椴恢�锟斤拷锟斤拷锟斤拷)锟斤拷锟节凤拷Rt锟斤拷锟斤拷锟斤拷锟斤拷tanA+tanB+tanC=tanAtanBtanC锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷影锟斤拷锟斤拷(锟街稱锟斤拷一锟斤拷锟揭讹拷锟斤拷)锟斤拷锟节★拷ABC锟叫ｏ拷a=bcosC+ccosB;b=ccosA+acosC;c=acosB+bcosA锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟轿冿拷锟叫圓锟诫徑r=2S/a+b+c(S锟斤拷锟斤拷e)锟斤拷锟斤拷訄A锟诫徑锟斤拷該锟斤拷知锟斤拷锟剿吧�锟矫凤拷锟斤拷锟剿癸拷锟斤拷锟斤拷锟斤拷OA1,B1锟斤拷C1锟街別锟角★拷ABC锟斤拷邊BC锟斤拷CA锟斤拷AB锟斤拷锟斤拷直锟斤拷锟斤拷锟较碉拷锟絚锟斤拷锟絫A1锟斤拷B1锟斤拷C1锟斤拷锟斤拷锟侥筹拷要锟絣锟斤拷锟斤拷CB1/B1A·BA1/A1C·AC1/C1B=1

46 . 锟斤拷锟絜锟絚

(5)锟斤拷锟斤拷锟斤拷锟斤拷锟�锟斤拷锟斤拷锟斤拷使锟矫碉拷锟絜位锟斤拷锟絧锟斤拷锟角达拷锟斤拷锟斤拷锟絜規(gu锟斤拷)锟杰凤拷锟斤拷锟斤拷锟节岋拷锟节讹拷锟斤拷锟絩锟斤拷锟斤拷锟斤拷锟斤拷锟�锟斤拷锟斤拷號锟饺等比旓拷锟斤拷锟斤拷锟�锟斤拷锟斤拷锟斤拷锟斤拷系锟斤拷;(6)锟斤拷锟斤拷锟叫筹拷锟斤拷變锟轿癸拷式锟斤拷锟斤拷锟�锟斤拷锟界：an=1/[n(n+2)]锟斤拷锟斤拷捅锟斤拷锟斤拷锟斤拷

47 . 锟斤拷锟絜锟絚

(7)锟斤拷锟斤拷未锟斤拷锟絔a1锟角凤拷锟斤拷细锟斤拷锟絪n-sn-1锟斤拷玫锟酵�項癸拷式;(8)锟斤拷锟叫诧拷锟斤拷锟角猴拷锟轿碉拷全锟絯锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷注锟斤拷锟斤拷锟叫撅拷锟斤拷锟叫碉拷锟斤拷值锟斤拷锟絵锟絕锟斤拷锟斤拷锟角凤拷取锟斤拷锟斤拷锟絵

48 . 锟斤拷锟絜锟絚

(9)锟斤拷锟斤拷锟斤拷锟絓锟姐不锟斤拷全锟饺價锟节达拷锟斤拷锟絓锟斤拷;(10)锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷模锟絓锟斤拷锟絕锟斤拷锟斤拷平锟斤拷之锟斤拷锟斤拷锟斤拷記锟絖锟斤拷锟斤拷锟斤拷锟斤拷锟紷锟絅锟絰锟斤拷锟絵锟叫筹拷锟斤拷锟斤拷锟紽2锟斤拷√2锟侥达拷…锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絰√2锟斤拷锟絰2锟侥撅拷锟斤拷锟斤拷锟絔锟斤拷锟絖锟斤拷;(11)锟酵旓拷锟侥幾猴拷锟斤拷锟絰锟斤拷锟斤拷锟斤拷

49 . 锟絇锟斤拷锟給锟斤拷锟角癸拷式

asint+bcost=[√(a²+b²)]sin(t+m)锟斤拷锟斤拷tanm=b/a[锟絣锟斤拷锟斤拷a>0]锟絝锟斤拷锟斤拷一些锟斤拷同锟絎锟斤拷锟絋去锟斤拷锟絔sinm锟斤拷锟斤拷cosm锟斤拷锟絖锟斤拷m锟斤拷锟斤拷锟斤拷锟絏锟斤拷锟紷锟斤拷太锟斤拷锟阶筹拷锟絜锟斤拷玫姆锟斤拷锟斤拷歉锟斤拷锟絫anm锟絖锟斤拷m.(見锟斤拷)锟斤拷锟絜锟斤拷锟絝锟斤拷锟斤拷sinx+√3cosx=2sin(x+m)锟斤拷锟斤拷锟絫anm=√3锟斤拷锟斤拷锟斤拷m=60锟斤拷锟斤拷锟斤拷锟斤拷原式=2sin(x+60锟斤拷)

50 . A锟斤拷B锟斤拷E锟紸x²/a²+y²/b²=1锟斤拷锟斤拷锟斤拷锟斤拷c锟斤拷锟斤拷OA锟斤拷直O(ji锟斤拷n)B锟斤拷锟絫锟斤拷1/锟絆OA锟絆²+1/锟絆OB锟絆²=1/a²+1/b²

锟斤拷锟斤拷锟斤拷锟絇锟斤拷锟絔锟斤拷

锟斤拷锟斤拷锟竭匡拷锟斤拷锟絎锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟铰高匡拷锟結訊锟斤拷锟竭匡拷锟斤拷锟斤拷锟斤拷锟斤拷前锟绞傦拷锟斤拷志愿锟斤拷锟�锟斤拷锟饺★拷謹锟斤拷锟斤拷锟�

锟竭匡拷锟絩锟絞锟斤拷锟斤拷全锟斤拷锟斤拷要锟斤拷(ji锟斤拷)锟絚

锟組锟斤拷"锟竭匡拷锟絎"微锟脚癸拷锟斤拷號