: hm(f (x'y+x) f (x' il)= f(x)-f (o)
Suyra a=g(sin a-kcosa)
(ii) lx +1)/k) : (/(*))'+./(r) - 1, vxe IR.
illn1
4,'.., L 4 .,'. t
i-t /\t)-t .-i /(i)+lTim lim (Sr+Sz). Tim lim (Sr+Sz).
Ldi gidi. Ki hiQu q, = .f (n),2 e N*.
Tt di6u kiQn cua bdi to6n ta c6 a1=2011,
an+1.a, = a3 + a, -lrYn> l. a?+a,-7
s,-s.=2f | :r*( 1
- I )
441
i-tai-l i-r\ai-t ait-l)
.( I r )
I r, - t a,,r -l )
= lim (S, -Sr) : 2
. ::-= _1. O
n--)+@ at -l 2010 1005
FNnl" x6t. Nhu da th6 hiQn 6 tr6n, bin ch6t cua bai to5n ndy li bdi to6n ddy sO vd d6y ld bdi to6n dey so
kh6ng kh6, nhrmg c6 nhi0u li lufn r6t ccv b6n. C5c b4n hgc sinh lop10,Jopl 1 sau c6 lcri gi6i tltng:
YOn Bii: Ngay€n Hdi Linh,l1T, THPT chuydn Nguydn
Tdt Thdnh; Bic Ninh: Trunng Giang Khang, l1Al,
TIIPT T{uSn Thdnh s6 l; Hung YEn: Hodng Vdn Duy, 10T1, Dd Thanh Tilng, 11T1, THPT chuyCn Hmg YCn;
Vinh Phrlc: DQng Quang Tudn, 17A7, THPT chuyOn
Vinh Phric; Hf,i Ducrng: Nguy€n Thi Thanh Y€n, l1T, THPT chuy6n Nguy6n Tr6i; NghQ An:. L€ Hgdng HiQp,
10A1, TIIPT Th6i Hda; Hodng Danh. Thdng, 7lAl,
THPT Qulnh Luu III; Hir finh: Trdn Qu6c Dilng,
llTl; Nguy€n MQU Thdnh, llT1, THPT chuy6n Hd
Tinh; Quf,ng Tri: HO Phudc Bdo,11T, TIIPT chuyOn
Le Quy D6n, Ddng Hd; Quf,ng Nam: Z€ Vil Vdn Phi,
11/1, TI{PT chuy6n Nguy6n Binh Khi6m.
NGUYEN MINH DUC
Suy ra en+t = = a, +l-)-
an an
Tri c6ng thic f6n, bing quy nap theo n,tathdy
ngay N77=q <az <q <...vd a, < 2010 + n,Vn 21. Cht i fu on-1co, vi PT gioi han a=a+l-!
a kh6ng c6 nghiOm tfurc thuQc (2011 ; +co). o Tri c6c nhdn xdt tr6n ta c6
oi-112009+i, Vi>1.
Docl6S,=f I ' A a, -l = i A 2009+iI -++cokhi
, (,,r\
n -) t<n (vi nhu ta d6 biet lim | ) ; I = +*). '-* \ i=t l7
Tucrng t.u Sz + +oo khi n -+ +@.
Nhuvdy lim(S1+Sr)=1o.
. K6t qui ld hay hon n6u :axdt lim (S1 - 52). n-++@
rhatvay s,-& =i(+-+) :i+
-r'f4-l a,+l) iq-lI I 4-1 I I 4-1 a;aiq ai ai+t-! ai+l 1 4-r 4-r a?-r 4-r 1 *BniLtl409. M\t B
tat nho A bdt diu
tt'tro't lr,r dinh Bctia mot kh6i hinh ctia mot kh6i hinh n1m BHC co dd_v"
Hf 2,lm vd g6c
H
BCH =a(hinh vd).
H€ so ma sal giira vat va mdt BC ld k:0,14.
Tinh gia tri ctia goc d img vdi thdi gian dixtrong tir B d€n C ld nho nhdt. Hoi^thdi gian xtrong tir B d€n C ld nho nhdt. Hoi^thdi gian a1' bdng bao nhi€u? Cho g: 9,8m/s2.
Loi gidi. Theo dfnh luflt II Newton ta c6
F+fr+F^,:mi (1)Trong d6 F: mi, Trong d6 F: mi, F., = kN. Chi6u phuong fixh (1) theo phucrng w6ng g6c vi song song vcri m{t pheng nghiOng, ta ducy. c mgcosa-N:0 mgsina-kN =ma
Suyra a=g(sin a-kcosa)1 1 ai*t -I 1 C ai-7 4 -l 111
a? *I ai -I ai*t -l . Boi vqy
(2) (3) (4)
ta nrr,r-ro0 T?S#E!
Thoi gian di xudng cira v6t tu B d5n C ld
ln
aphilithda m6n di6u kiqn lU '" ', (6)