Giáo trình toán cao cấp 1

69 VO THJ THANH HA (Chu bien) LE VAN LAI , ~ TOAN CAO CAP TRUONG DAI HOC CONG NGl1l~P TP.HC~ - HU VIE · A C,.G MA V~CH : NHA XUAT BAN DAI HOC CONG NGHIEP • • • THANH PHO HO CHI MINH ' LO'i n6i dau Duqc sv ch&p thu~n cua Ban Ciam hi~u truong Dqi h9c Cong nghi~p Thanh ph6 H6 Chi Minh va Truong khoa Khoa h9c Co ban, giao trinh Toan cao c&p duqc bien SOqn nham phvc vv cho vi~c dqy va h9c mon Toan cao c&p tqi truong Ciao trinh duqc bien SOqn danh cho sinh vien dqi h9c kh6i ky thu~t va kinh t~ N()i dung giao trinh duqc chung toi bien SOqn theo chuong trinh dao tqo mon Toan cao c&p tqi truong Dqi h9c Cong nghi~p Thanh ph6 H6 Chi Minh, ki~n thuc duqc trinh bay m()t each logic, de hieu Moi n()i dung ki~n thuc d~u c6 vi dv minh h9a cho sinh vien ti~p thu m()t each de dang Sau moi chuong d~u c6 phcln bai t~p tv lu~n va tr~c nghi~m de sinh vien luy~n t~p Sinh vien c6 the tim th&y dap an ho~c huong dan nhfrng trang cu6i Ciao trinh duqc chia nam chuong: Chuong 1: Cioi hqn va lien tvc Chuong 2: Dqo ham va vi phan Chuong 3: Tich phan Chuong 4: Chuoi s6 Chuong 5: Phep tinh vi phan ham nhi~u bi~n Tac gia xin gui loi cam on chan d~n Ban Ciam hi~u truong Dqi h9c Cong nghi~p Thanh ph6 H6 Chi Minh va Chu nhi~m Khoa Khoa h9c co ban da tqo m9i di~u ki~n thu~n lqi de giao trinh duqc xu&t ban D6ng thoi chung toi xin duqc chan cam on quy thcly, co t6 Toan thu()c Khoa Khoa h9c Co ban - Truong Dqi h9c Cong nghi~p ph6 H6 Chi Minh da d9c ban thao va dong g6p nhi~u y ki~n quy bau Tac gia hy v9ng rang giao trinh se la nguoi bqn d6ng hanh va giup ich nhi~u cho sinh vien va giang vien qua trinh dqy va h9c mon Toan cao c&p Tran tr9ng! Thanh ph6 H6 Chi Minh, thang 10 nam 2022 Cac tac gia Trang thOng tin giao trinh https://github.com/khoacoban/toancaocap1 Nham t9-o c~u n6i gifra cac tac gia va b9-n d9c, chung toi da thi~t l~p trang thong tin ho trq t9-i dta chi tren trang chung toi se: Cung c~p cac chtrng minh: Nham trinh bay ki~n thuc m◊t each co d9ng va hieu, chung toi da luqc b6 cac chung minh ban in va cung c~p ban di~n tu B9-n d9c quan tam d~n cac chung minh c6 the tim day de Thong tin sai sot: Trong l~n d~u phat hanh, chung toi khong the tranh khoi nhfrng sai s6t Do d6, chting toi se dang cac ban dinh chinh t9-i trang thong tin Ti~p nh~n phan h6i d9c gia: Tac gia ciing mong nh~n duqc nhi~u y ki~n dong g6p quy bau tu quy th~y, co va cac b9-n sinh vien de l~n tai ban sau duqc hoan thi~n hon Cac tac gia Muc luc • • Loi n6i d§.u Trang thong tin giao trinh M1:1-c 11:1-c GIOI H~N VA LIEN T{JC 1.1 BAN THlJC 1.1.1 Cac t~p s6 thuong g~p 1.1.2 Tien d~ v~ sup, inf 1.1.3 Tinh ch§.t Archimede 1 T~p s6 thvc m6 n)ng 1.2 HAMSO 1.2.1 Khai ni~m ham s6 1.2.2 M x voi m9i x E A Khi A co m(>t ch~n tren, ta n6i A bi ch~n tren va d6, ph§.n tu nh6 nh§.t cua t~p t§.t ca cac ch~n tren, n~u c6, duqc g9i la ch~n tren nh6 nhdt cua A, ky hi~u la sup A • a la phdn tu Zan nhdt cua A neu a E A va a > x voi m9i x E A Ph§.n tu Ion nh§.t cua A, n~u c6, thi nh§.t va duqc ky hi~u la max A Trang 82 ChU'ctng H~ phU'ctng trinh tuy~n tinh Bai t~p 2.4 Bi~n lu~n s6 nghi~m cac h~ phuong trinh thu§.n nh~t sau: a rm+ l)x- my =0 =0 mx+ 4y b x+2y- 2z = 2x+4y- Sz = 3x + 6y + mz = c 3y2x+ z=0 4x + (m + S)y + (m - 3)z = 12y+ (m-4)z = Bx+ 2.5.2 d mx+ y+ z+ t=0 x+my+ z+ t=0 x+ y+mz+ t=0 x+ y+ z +mt= e 2y + Z + 2t = x+ y- z +mt= X + 7y-5z t=0 X - Bai t~p tric nghi~m chuang N(>i dung Giai h~ phU'ctng trinh tuy~n tinh x+y+z=0 2x + 3y + z = 3x +4y+3z = Cau 2.1 Giai h~ phuong trinh A x = -1, y = 1, z = B x = -a - /3, y = a, z = /3; a/3 E lR C x = -1 - 2a, y = + a, z = a; a E lR D x = -1 - a1 y = 1, z = a; a E lR 2x+3y+3z = Cau 2.2 Giai h~ phuong trinh x - 2y + z = 3x+ y+4z = A x = -3(a + /3)/2, y = a z = /3; a/3 E lR B x = 3,y = z = -2 C • x = J7 - 2a a E lR y = _i7 - la z = a· D x = + 9a y = a z = -2 - 7a; a E lR 1 1 I 2x + 3y - 2z = { 2x + Sy - 2z = · A x = - 3a + 2/3 y = a z = /3; a /3 E lR B x = + a y = z = a; a E lR C x = - a, y = -a, z = a; a E lR D x = 2,y = 1,z = Cau 2.3 Giai he phuong trinh 1 1 2.5 Bai t~p chtre1ng Trang 83 x+y- z=2 Cau 2.4 Giai h~ phuong trinh A x = B x = C x = D x = y - 3z =1 y-4z =3 5, y = -5, z = -2 + 2tX, y = - tX, z = a; a E R + 2tX, y = - tX, z = tX; a E R -1, y = + 2a, z = 0, tX E R y+2z = Cau 2.5 Giai h~ phuong trinh 3x - 2y - z = 4x -3y + z = X - A x = + tX - 2{3, y = tX, z = /3; tX, f3 E R B x = - - 9a, y = -3 + 7a, z = a; tX E R C X = -2,y = -3,z = D H~ phuong trinh vo nghi~m X Cau 2.6 Giai h~ phuong trinh + 2y-2z = 2x + Sy - Sz = 3x + 7y- 7z = A x = - 2a, y = 2, z = + a; tX E R B x = -2, y = + tX, z = tX; a E R C x = - 2a, y = + a, z = a; tX E R D x = - 2, y = 2, z = Cau 2.7 Giai h~ phuong trinh x- y+2z=3 { -x +2y + z = A x = + tX - 2{3, y = tX, z = /3; tX, f3 E R B x = - 2a, y = 0, z = a; tX E R C x = + tX, y = -(X, z = -tX; a E R D x = - Sa, y = - 3a, z = tX ; tX E R 3x+4y-3z = Cau 2.8 Giai h~ phuong trinh 4x + 7y - 4z = 2x +3y-2z = A x = a/2,y = a/2,z = -2/3; tX ER B.x=O,y=-1,z=-2; aER C x = tX - 2, y = 2, z = a; tX E R D x = a - 2,y = 5,z = a; tX ER Cau 2.9 Giai he phuong trinh · x+3y+2z { 2x- y+3z =0 =0 Trang 84 ChU'O'ng H~ phU'O'ng trinh tuy~n tinh 117 t1y l Ax • 71z - t tEJR • B x = - 1.Jt,y = -~t1z = t t E JR C.x=1.Jt 1y=~ 1z=t tEJR 117 t1 y- - l zt tEJR • Dx • 71 x+ y- z=O Cau 2.10 Giai h~ phuong trinh 2x + 4y- 2z =4 2x + 3y + 2z = A x = a/21y = a/21z = a; a E JR B x = y = z = C x = a - 21y = 21z = a; a E JR D x = -2, y = 21 z = 1 x-y- z=3 Cau 2.11 Giai h~ phucJng trinh 2x + y - 2z = 5x + y-5z =3 A x = + a + /31 y = a 1z = /3; a 1/3 E JR B x = l + a 1y = -21z = a; a E JR C x = l y = -2 z = D H~ phuong trinh v6 nghi~m 1 5x + l2y - 12z =2 Cau 2.12 Giai h~ phuong trinh 2x + Sy - 5z = 3x + 7y- 7z = A x = - - 2a y = a z = l + a; a E JR B x = -21 y = l + a z = a; a E JR C x = - + a y = l + a z = a; a E JR D x = -21 y = l1 z = 3y + 4z =1 Cau 2.13 Giai h~ phuong trinh 2x - 6y + 8z = X - 5x - l5y + 20z = A.x=l+17a1y=7a 1z=a; aEJR B.x=l-17a 1y=7a 1z=a; aEJR C x = l y = z = D x = + 3a1 - 4a21 y = a11 z = a2; a11 a2 E JR 1 x- y-2z=0 Cau 2.14 Giai h~ phucJng trinh y + 4z =2 2x -2y-5z =0 x + Trang 85 2.5 Bai t~p ch1.t