Sách bài tập đại số và giải tích 11 cơ bản

v u TUAN (Chu bien) - TRAN VAN HAO OAO NGOC NAM - LE VAN TIEN -IVU VIET YEN BAI TAP y ,»;p7X*"^' ,•• * • • • \ ;»vr*»« ' ' • • • • • • Ơ ằ. T' ai'' a NHA XUAT BAN GIAO DUC VIET NAM VU TUAN (Chu bien) TRAN VAN HAO - BAG NGOC NAM LEVANTI^N-VUVI^TYEN BAITAP DAIS6 VAGIAI TICH (Tdi bdn ldn thd tu) r NHA XUAT BAN GIAO DUC VIET NAM Ban quy^n thu6c Nha xu^t ban Giao due Vi6t Nam 01 - 201 l/CXB/824 - 1235/GD Ma s6': CB103T1 m.' huang L HAM SO Ll/ONG GIAC PHUONG TRINH Ll/ONG GIAC §1 Ham so laong giac A KIEN THCTC CAN NHd Ham so sin Ham s6' j = sinx co tap xae dinh la M va -1 < sinjc < 1, Vx G R y = sin X la ham s6' le y = sinx la ham s6' tu^n hoan v6i chu ki 2jt Ham s6 y = sinx nhan cae gia tri dac bi6t: • sinx = x = kn, k e Z n • sm X = x = — + k2n, k G Z • sinx = -1 x = -— + k2n, k e Z D6 thi ham s6 y = sinx (H.l) : Hinh Ham so cosin Ham s6' y = cosx eo tap xae dinh la R va -1 < cosx < 1, Vx G y = cosx la ham so ehSn y = cosx la ham so tu^n hoan vdi chu ki 2n Ham s6' y = cosx nhan cac gia tri dac bi6t: • cosx = X = — + kn, k eZ • cos X = X = k2n, k e Z • cosx = -1 X = {2k + l)7i, k e It D6 thi ham s6' y = cosx (H.2) : Hinfi Ham so tang Ham sd V = tanx = eo tap xae dinh la cosx D = R\{^ + kn,ke y = tanx la ham s6 le y = tanx la ham sd tu5n hoan vdi chu ki n Ham sd y = tar v nhan eae gia tri dae biet: • tanx = x =kn, k e Z • tanx = X = n— + kn, k e.Z • tanx = -1 x = -— + kn, k G D6 thi ham sd 3^ = tanx (H.3): -37t Hinh Ham so cotang COSX Ham s6 y = coix = —— c6 tap xae dinh la smx D= R\{kTi,keZ] y = cotx la ham sd le y = coix la ham sd tuSn hoan vdi chu ki % Ham sd y = cot x nhan cac gia tri dac bi6t: 71 • cot X = X = — + kn, k e Z 71 • cot X = X = — + ^71, k eZ It, • cotx = -1 X = —— + ^7r, )t G Z D6 thi ham sd j = cotx (H.4): O -27t ]£2 Hinh B Vi DU • Vidul Tim tap xae dinh cua eae ham sd a) y = sin3x ; b) y = cos— ; X c) y = cosVx ; d) y = sin 1+X 1-x" Gidi a) Dat t = 3x, ta duoc ham sd y = sin r co tap xae dinh la D = R Mat khae, rGRx = - G R nfen tap xae dinh eua ham s6 y = sin3x la R ' • b) Ta CO — e R X ;^ Vay tap xae dinh eiia ham sd y = cos— la X ^ D = R\{0} e) Ta CO Vx G R o x > Vay tap xae dinh cua ham s6 y = cosVx la D = [0 ; +00) d ) T a CO + ^ 1-X ir» l + ^ ,^ G R 0 « 1-x 1+X vay tap xae dinh eua ham sd j = sin J-j 1^ - < X < la D = [-1 ; 1) • Vidul Tim tap xae dinh eua cae ham sd a) y = ; ^ 2cosx b) y = cot 2x - — , , ' ^ y A)' cotx ,^ sinx+ Gidi , K a) Ham sd y = x^c dinh va ehi cosx ^ hay x ?t — + kn, k G ' ^ • 2cosx • • vay tap x^e dinh cua ham sd la D = R \ { | + itTi, A: G I 71 I \ Aj 7C b) Ham sd y = cot 2x - — xae dinh va chi 2x - — ^t kn, k G • , hay x * — + k—, k e Z o vay tap xae dinh cua ham sd y = cot 2x - — la D = R \ { | + ^|,A:G e) Ham sd y = cotx ^ , [sinx 9^0 xae dmh < cosx-1 • lcosx?tl lx^kn,keZ < Ix^t A:27i,;tGZ Tap {^27:, k &Z] la tap eua tap [kn, k eZ} (umg vdd cac gia tri k cot X chan) vay tap xae dinh cua ham sd la cosx-1 R\{kn,k€Z] D= sinx + d) Bieu thiie ludn khdng am va no eo nghla cosx + 15«t 0, hay cosx + " cosx 9t - vay ta phai c6 x ^ (2k + l)n, it G Z, do tap xae dinh cua ^ smx+ ham so y = J la ^'cosx + D = R\{(2A: + l)7i, A;GZ} • Vi dn ? Tim gia tri ldn nhS^t va gia tri nho nha't cua cac h£im sd : b) y = - sin X cos x ; a) y = + 3eosx ; c)y= l + 4cos^x ; d) y = 2sin x - cos2x Gidi a) Vl -1 < cosx < ndn -3 < 3eosx < 3, do - < + 3cosx < vay gia tri ldn nha't eua ham sd' la 5, dat duoc cosx = o X = 2kn, keZ Gia tri nho nha't cua ham sd la - , dat duoc cos x = -1 d' x = {2k + l)7t, keZ b) y = - 4sin^ xcos^ x = - (2sinxcosx)^ = - sin^ 2x Ta ed < sin^ 2x < nen -1 < -sin^ 2x < vay 2 limx„ = l ( - ) = - 21 a) Day (x„) bi chan vi n 5/22 < -^; < voi moi n ; rf +3 b) Day (y„) bi chan vi 2/2 \yn\ = (-1)" n+l e) Day (z„) khdng bi chdn vi |z„| = l/2COSrtTCl = /2 234 , , I sia/21 < 2/2 7 ^„ Mat khdc, day sd bi chdn tren vi x„ •" 1 1 1 -T + - + = - r + + + 5" + -oo [ • x|4 + - 25 a) lim smx - sma x-ya X-a x-a X +a cos —-— sm —-— 2 Um = cosa x-a b) Ddt - X = r (r ^ X -)• 1), ta cd lim(l - x)tan-— = lun rtan(l - i)— x-^\ x->0 1 = Um/cot—f = Um ——^ 2->0 f->0 ^ 71 tan-r 236 2^ Tl" = +00 ^ Chu y lim tanx Jc->0 X lim sinx X COSX Jf->P = c) + V3 5-3V3' d) , t a n x - s i n x , 1-cosx Um = lim — I x-*o sin X x^o sin x cos x a) 2(1 - 2x) 2sin^= lim x^O • 2X 2X 4sm —cos —cosx 2 1 ( l - X + x2)2 b) 12 - 6x - 6x2 + 2x^ + 5x^ - 3x^ (1-^)^ c) d) e) f) -2eosx(l + sinx) + cos X 2sin^x 2x X -—sin-^i-tan— 3 cosI 2x - — n sm x - 27 A = Khi dd/(x) ed dao hdm tai x = 237 MUC LUC Trang Chumg / HAM SO LUDNG GIAC - PHUGNG TRINH LlTONG GIAC § Hdm sd Iflgng gidc §2 Phuong trinh lugng gidc CO ban 13 §3 Mdt sd phuong trinh lugng gidc thudng gap 24 Bdi tdp dn chuong I 35 Ldi giai - Hudng ddn - Dap sd chuong I 36 Chuang II TO HOP - XAC SUAT 57 §1 Quy tic ddm 57 §2 Hodn vi, chinh hgp, td hgp 60 §3 Nhi thflc Niu-ton 64 §4 Phep thfl va bidn cd 66 §5 Xdc sudt cua bidn cd 69 Bdi tdp dn chuong II 73 Ldi giai - Hudng ddn - Dap sd chuong II 74 Chuang IIL 238 DAY SO - C ^ SO CONG VA CAP SO NHAN 87 § Phuong phdp quy nap toan hgc 87 §2 Day sd 96 §3 Cdp sd cdng 107 §4 Cdp sd nhdn 114 Bai tdp dn chuong III 121 Ldi giai - Hudng ddn - Dap sd chuong III 124 Chumg IV Gldl HAN 140 § Gidi han cua day sd 140 §2 Gidi han cua ham sd 151 §3 Ham sd lidn tuc 160 Bdi tdp dn chuong IV 165 Ldi giai - Hudng ddn - Ddp sd chuong IV 170 Chumg V DAO HAM 190 § Dinh nghia vd y nghia eua dao ham 190 §2 Cdc quy tic tinh dao ham 195 §3 Dao ham cua cae ham sd lugng giac 199 §4 Vi phdn 203 §5 Dao hdm cdp hai 205 Bdi tdp dn chuong V 207 Ldi giai - Hudng ddn - Dap sd chuong V 209 On tdp cud'i ndm 220 239 Chiu trach nhiem xudt bdn : Chu tich HDQT kiem T6ng Giam d6c NGO TRAN AI Pho Tdng Giam d6'c kiem T6ng bidn tap NGUYfeN Q U t THAO Bien tap ldn ddu: NGUYfiN XUAN BINH - NGUYfiN NGOC TU Bien tap tdi bdn : NGUYfeN XUAN BINH Bien tap Id thuat: NGUYfeN THANH THUt - TRAN THANH HANG Trinh bdy bia : TRAN THUt HANH Sih bdn in : Lfe THI THANH HANG Che bdn : C N G TY CF THifeT KE VA PHAT HANH SACH GIAO DUC BAI TAP DAI SO VA GIAI TICH 11 Ma so : CB103T1 In 35.000 cudn, khd 17 x 24 cm In tai Cdng ty TNHH MTV in Quang Ninh Sd in: 2134 So xuat ban: 01-2011/CXB/824-1235/GD In xong va nop luu chieu thang nam 2011 240 •u< V I / O N G M I E N KIM CUdNG CHAT LUONG QUOC TE HUAN CHKONG HO CHI MINH SACH BAIlAPLCfP 11 BAI TAP DAI so VA GIAI TICH 11 BAI TAP HiNH HOC 11 BAI TAP NGO" VAN 11 (tap mot, tap hai) BAITAPVATLIU BAlTAPUCHSCfll BAI TAP HOA HOC 11 10 BAI TAP TIENG ANH 11 BAI TAP SINH HOC 11 11.BAITAPTIENGPHAP11 B A I T A P O I A U ' H 12 BAI TAP TIENG NGA 11 BAI TAP TIN HOC 11 SACH BAI TAP LCfP 11 - N A N G CAO BAI TAP OAI so VA GIAI TiCH 11 , BAI TAP HOA HOC 11 BAI TAP HiNH HOC 11 , BAI TAP N G U V A N 11 (tap mot, tap hai) BAI TAP VAT LI 11 , BAI TAP TIENG ANH 11 Ban doc co the mua sach tai: • • • • Cac Cong ty Sach - Thiet bi truong hoc a cac dia phucmg Cong ty CP Dau tu va Phat triSn Giao due Ha Noi, 187B Giang Vo, TP Ha Noi • Cong ty CP Dau tu va Phat trien Giao due Phuang Nam, 231 Nguyen Van Cu, Quan 5, TP HCM Cong ty CP Dau tu va Phat trien Giao due Da Nang, 15 Nguyen Chi Thanh, TP Da Nang hoac cac cua hang sach cua Nha xuat ban Giao due Viet Nam : - Tai TP Ha Noi : - Tai - Tai - Tai Tai 187 Giang V6 ; 232 Tay Son ; 23 Trang Tien ; 25 Han Thuyen : 32E Kim Ma ; 14 Nguyen Khanh Toan ; 67B Cua Bae TP Da Nang : 78 Pasteur ; 247 Hai Phong TP H6 Chi Minh 104 Mai Thi Luu ; 2A Dinh Tien Hoang, Quan ; 240 Tran Binh Trong ; 231 Nguyin Van Cir, Quan TP can Tho : 5 Duong 30'4 Website ban sach true tuyen : www.sach24.vn Website: www.nxbgd.vn 934994 " 023658 Gia: 12.400d ... tiing, se duge dd thi ham sd tren doan [-27t; 27r] Dd thi ham sd duoc bidu dien tren hinh Hinh 11 X X cos—, ndu cos— > 2 X b) Ta cd cos— X X -cos—, ne'u cos— < 2 Vi vay, tit dd thi ham sd y =... t G ô 2x = - - 60° + it360°, it G X = 5° + /:180°, it G Z