C\u00e2u h\u1ecfi 6 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0Ph\u00e1t bi\u1ec3u \u0111\u1ecbnh l\u00ed v\u1ec1 quy t\u1eafc logarit, c\u00f4ng th\u1ee9c \u0111\u1ed5i c\u01a1 s\u1ed1.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\u2022 Quy t\u1eafc t\u00ednh logarit<\/strong><\/p>\n

<\/p>\n

\u2022 \u0110\u1ed5i c\u01a1 s\u1ed1<\/strong><\/p>\n

<\/p>\n

C\u00e2u h\u1ecfi 7 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0N\u00eau t\u00ednh ch\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 m\u0169, h\u00e0m s\u1ed1 logarit, m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 m\u0169 c\u00e0 h\u00e0m s\u1ed1 logarit c\u00f9ng c\u01a1 s\u1ed1.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

1. H\u00e0m s\u1ed1 m\u0169<\/strong><\/p>\n

Cho s\u1ed1 a > 0, a \u2260 1. H\u00e0m s\u1ed1 y = a^{x<\/sup>\u00a0\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m s\u1ed1 m\u0169 c\u01a1 s\u1ed1 a.<\/p>\n}

Kh\u1ea3o s\u00e1t:<\/p>\n

* D = R.<\/p>\n

* N\u1ebfu:<\/p>\n

– a > 1: h\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn<\/p>\n

– 0 < a < 1: h\u00e0m s\u1ed1 lu\u00f4n ngh\u1ecbch bi\u1ebfn<\/p>\n

* \u0110\u1ed3 th\u1ecb lu\u00f4n \u0111i qua hai \u0111i\u1ec3m ( 0; 1) v\u00e0 (1; a) c\u00f3 ti\u1ec7m c\u1eadn ngang l\u00e0 tr\u1ee5c Ox.<\/p>\n

2. H\u00e0m Logarit<\/strong><\/p>\n

Cho s\u1ed1 a > 0, a \u2260 1 . H\u00e0m s\u1ed1<\/p>\n

<\/p>\n

\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m logarit c\u01a1 s\u1ed1 a.<\/p>\n

Kh\u1ea3o s\u00e1t:<\/p>\n

* D = (0;+\u221e)<\/p>\n

* N\u1ebfu:<\/p>\n

– a > 1: H\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng bi\u1ebfn tr\u00ean D<\/p>\n

– 0 < a < 1: h\u00e0m s\u1ed1 lu\u00f4n ngh\u1ecbch bi\u1ebfn<\/p>\n

* \u0110\u1ed3 th\u1ecb lu\u00f4n \u0111i qua hai \u0111i\u1ec3m (1; 0) v\u00e0 (a; 1) c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 tr\u1ee5c Oy.<\/p>\n

\u2022 Li\u00ean h\u1ec7 gi\u1eefa \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 m\u0169 v\u00e0 h\u00e0m s\u1ed1 logarit c\u00f9ng c\u01a1 s\u1ed1: \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 m\u0169 v\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 logarit \u0111\u1ed1i x\u1ee9ng nhau qua \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c ph\u1ea7n t\u01b0 th\u1ee9 nh\u1ea5t.<\/p>\n

C\u00e2u h\u1ecfi 8 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0N\u00eau \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u00ednh nguy\u00ean h\u00e0m.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

Nguy\u00ean h\u00e0m<\/strong><\/p>\n

Cho h\u00e0m s\u1ed1 f(x) x\u00e1c \u0111\u1ecbnh tr\u00ean K ( k l\u00e0 n\u1eeda kho\u1ea3ng hay \u0111o\u1ea1n c\u1ee7a tr\u1ee5c s\u1ed1). H\u00e0m s\u1ed1 F(x) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) tr\u00ean K n\u1ebfu F\u2019(x) = f(x) v\u1edbi m\u1ecdi x thu\u1ed9c K.<\/p>\n

Ph\u01b0\u01a1ng ph\u00e1p t\u00ednh nguy\u00ean h\u00e0m<\/p>\n

* \u0110\u1ed5i bi\u1ebfn s\u1ed1:<\/strong><\/p>\n

<\/p>\n

C\u00e2u h\u1ecfi 9 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0N\u00eau \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u00ednh t\u00edch ph\u00e2n.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\u2022 \u0110\u1ecbnh ngh\u0129a<\/strong><\/p>\n

Cho h\u00e0m s\u1ed1 y = f(x) li\u00ean t\u1ee5c tr\u00ean [a; b] , F(x) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a f(x) tr\u00ean [a; b]. Hi\u1ec7u s\u1ed1 F(b) \u2013 F(a) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u00edch ph\u00e2n t\u1eeb a \u0111\u1ebfn b c\u1ee7a h\u00e0m s\u1ed1 f(x)<\/p>\n

<\/p>\n

\u2022 Ph\u01b0\u01a1ng ph\u00e1p t\u00ednh t\u00edch ph\u00e2n<\/p>\n

a) \u0110\u1ed5i bi\u1ebfn s\u1ed1:<\/strong><\/p>\n

\u0110\u1ecbnh l\u00ed 1: Cho h\u00e0m s\u1ed1 f(x) li\u00ean t\u1ee5c tr\u00ean [a; b]. Gi\u1ea3 s\u1eed h\u00e0m s\u1ed1 x = \u03c6(t) c\u00f3 \u0111\u1ea1o h\u00e0m li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [ \u03b1;\u03b2] sao cho \u03c6(\u03b1) = a; \u03c6(\u03b2) = \u03b2v\u00e0 a \u2264 \u03c6(t) \u2264 b v\u1edbi m\u1ecdi t \u2208 [\u03b1;\u03b2]. Khi \u0111\u00f3:<\/p>\n

<\/p>\n

b) T\u00edch ph\u00e2n t\u1eebng ph\u1ea7n<\/strong><\/p>\n

N\u1ebfu u = u(x) v\u00e0 v = v(x) l\u00e0 hai h\u00e0m s\u1ed1 c\u00f3 \u0111\u1ea1o h\u00e0m li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [a; b] th\u00ec:<\/p>\n<\/div>\n

 <\/p>\n

<\/p>\n

C\u00e2u h\u1ecfi 10 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0Nh\u1eafc l\u1ea1i \u0111\u1ecbnh ngh\u0129a s\u1ed1 ph\u1ee9c, s\u1ed1 ph\u1ee9c li\u00ean h\u1ee3p, m\u00f4 \u0111un c\u1ee7a s\u1ed1 ph\u1ee9c. Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc c\u1ee7a s\u1ed1 ph\u1ee9c.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

1. S\u1ed1 ph\u1ee9c<\/strong><\/p>\n

M\u1ed7i bi\u1ec3u th\u1ee9c d\u1ea1ng a + bi, trong \u0111\u00f3: a, b \u2208 R;i^{2<\/sup>= -1 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 s\u1ed1 ph\u1ee9c. Trong \u0111\u00f3 a \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u1ea7n th\u1ef1c, b g\u1ecdi l\u00e0 ph\u1ea7n \u1ea3o, s\u1ed1 i l\u00e0 \u0111\u01a1n v\u1ecb \u1ea3o.<\/p>\n}

2. M\u00f4 \u0111un<\/strong><\/p>\n

Cho s\u1ed1 ph\u1ee9c z = a + bi, \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi \u0111i\u1ec3m M(a;b) tr\u00ean t\u1ecda \u0111\u1ed9 Oxy. Ta g\u1ecdi m\u00f4 \u0111un c\u1ee7a s\u1ed1 ph\u1ee9c z, k\u00ed hi\u1ec7u l\u00e0 |z| l\u00e0 \u0111\u1ecd d\u00e0i c\u1ee7a vect\u01a1 OM.<\/p>\n

<\/p>\n

3. S\u1ed1 ph\u1ee9c li\u00ean h\u1ee3p<\/strong><\/p>\n

Cho s\u1ed1 ph\u1ee9c z = a + bi, ta g\u1ecdi a \u2013 bi l\u00e0 s\u1ed1 ph\u1ee9c li\u00ean h\u1ee3p c\u1ee7a z<\/p>\n

<\/p>\n

B\u00e0i 1 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1 f(x)=ax^{2<\/sup>-2(a+1)x+a+2 (a \u2260 0)<\/span><\/strong><\/p>\n}

a) Ch\u1ee9ng t\u1ecf r\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh f(x)=0 lu\u00f4n c\u00f3 nghi\u1ec7m th\u1ef1c. T\u00ednh c\u00e1c nghi\u1ec7m \u0111\u00f3.<\/span><\/strong><\/p>\n

b) T\u00ednh t\u1ed5ng S v\u00e0 t\u00edch P c\u1ee7a c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f(x) =0. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a S v\u00e0 P theo a.<\/span><\/strong><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean:<\/strong><\/p>\n

<\/p>\n

\u0110\u1ed3 th\u1ecb (h\u00ecnh thang tr\u00ean).<\/strong><\/p>\n

<\/p>\n

\u0110\u1ed3 th\u1ecb ( h\u00ecnh tr\u00ean).<\/strong><\/p>\n

<\/p>\n

B\u00e0i 2 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

B\u00e0i 3 (trang 146 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1 y = x^{3<\/sup>\u00a0+ ax2<\/sup>\u00a0+ bx+1<\/strong><\/span><\/p>\n}

a) T\u00ecm a v\u00e0 b \u0111\u1ec3 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111i qua hai \u0111i\u1ec3m: A(1;2)v\u00e0 B(-2;-1).<\/strong><\/span><\/p>\n

b) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (C ) c\u1ee7a h\u00e0m s\u1ed1 \u1ee9ng v\u1edbi c\u00e1c gi\u00e1 tr\u1ecb t\u00ecm \u0111\u01b0\u1ee3c c\u1ee7a a v\u00e0 b.<\/strong><\/span><\/p>\n

c) T\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3 tr\u00f2n xoay thu \u0111\u01b0\u1ee3c khi quay h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u01b0\u1eddng y = 0, x = 0, x = 1 v\u00e0 \u0111\u1ed3 th\u1ecb (C ) xung quanh tr\u1ee5c ho\u00e0nh.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

B\u00e0i 4 (trang 146 SGK Gi\u1ea3i t\u00edch 12):\u00a0X\u00e9t chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi ph\u01b0\u01a1ng tr\u00ecnh:<\/strong><\/span><\/p>\n

Trong \u0111\u00f3 t \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng gi\u00e2y v\u00e0 S \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng m\u00e9t.<\/strong><\/span><\/p>\n

a) T\u00ednh v(2), a(2), bi\u1ebft v(t), a(t) l\u1ea7n l\u01b0\u1ee3t l\u00e0 v\u1eadn t\u1ed1c v\u00e0 gia t\u1ed1c chuy\u1ec3n \u0111\u1ed9ng \u0111\u00e3 cho.<\/strong><\/span><\/p>\n

b) T\u00ecm th\u1eddi \u0111i\u1ec3m t m\u00e0 t\u1ea1i \u0111\u00f3 v\u1eadn t\u1ed1c b\u1eb1ng 0.<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

Theo \u00fd ngh\u0129a c\u01a1 h\u1ecdc c\u1ee7a \u0111\u1ea1o h\u00e0m ta c\u00f3:<\/p>\n

v(t)=s^{‘<\/sup>(t)=t3<\/sup>-3t2<\/sup>+t-3<\/p>\n}

v(2)=2^{3<\/sup>-3.22<\/sup>+2-3=-5 (m\/s)<\/p>\n}

a(t)=v^{‘<\/sup>(t)=s”<\/sup>(t)=3t2<\/sup>-6t+1<\/p>\n}

a(2)=3.2^{2<\/sup>-6.2+1=1 (m\/s2<\/sup>)<\/p>\n}

v(t)=t^{3<\/sup>-3t2<\/sup>+t-3=0<\/p>\n}

(t-3)(t^{1<\/sup>+1)=0 => t = 3<\/p>\n}

V\u1eady th\u1eddi \u0111i\u1ec3m t_{o<\/sub>=3s th\u00ec v\u1eadn t\u1ed1c b\u1eb1ng 0.<\/p>\n}

B\u00e0i 5 (trang 146 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1 y = x^{4<\/sup>\u00a0+ a4<\/sup>\u00a0+ b<\/strong><\/span><\/p>\n}

a) T\u00ednh a, b \u0111\u1ec3 h\u00e0m s\u1ed1 c\u1ef1c tr\u1ecb b\u1eb1ng 3\/2 khi x =1.<\/strong><\/span><\/p>\n

b) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho khi:<\/strong><\/span><\/p>\n

a=-1\/2,b=1<\/strong><\/span><\/p>\n

c) Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ee7a (C) t\u1ea1i c\u00e1c \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng 1.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

B\u00e0i 6 (trang 146 SGK Gi\u1ea3i t\u00edch 12):<\/strong><\/span><\/p>\n

<\/strong><\/span>a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (C ) c\u1ee7a h\u00e0m s\u1ed1 khi m = 2.<\/strong><\/span><\/p>\n

b) Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn d c\u1ee7a \u0111\u1ed3 thi (C ) t\u1ea1i \u0111i\u1ec3m M c\u00f3 ho\u00e0nh \u0111\u1ed9 a \u2260 -1.<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

B\u00e0i 7 (trang 146 SGK Gi\u1ea3i t\u00edch 12):\u00a0Cho h\u00e0m s\u1ed1<\/strong><\/span><\/p>\n

<\/p>\n

 <\/p>\n

a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb (C ) c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho.<\/p>\n

b) T\u00ecm giao \u0111i\u1ec3m c\u1ee7a (C ) v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y=x^{2<\/sup>+1 . Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ee7a (C ) t\u1ea1i m\u1ed7i giao \u0111i\u1ec3m.<\/p>\n}

c) T\u00ednh th\u1ec3 t\u00edch v\u1eadt tr\u00f2n xoay thu \u0111\u01b0\u1ee3c khi h\u00ecnh ph\u1eb3ng H gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb (C ) v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng y = 0; x = 1 xung quanh tr\u1ee5c Ox.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\u00a0<\/p>\n

<\/p>\n

B\u00e0i 8 (trang 147 SGK Gi\u1ea3i t\u00edch 12):\u00a0T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1:<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

B\u00e0i 9 (trang 147 SGK Gi\u1ea3i t\u00edch 12):\u00a0Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh sau:<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

 <\/p>\n

<\/p>\n

B\u00e0i 10 (trang 147 SGK Gi\u1ea3i t\u00edch 12):\u00a0Gi\u1ea3i c\u00e1c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh sau:<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

B\u00e0i 11 (trang 147 SGK Gi\u1ea3i t\u00edch 12):\u00a0T\u00ednh c\u00e1c t\u00edch ph\u00e2n sau b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p t\u00edch ph\u00e2n t\u1eebng ph\u1ea7n:<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

B\u00e0i 12 (trang 147 SGK Gi\u1ea3i t\u00edch 12):\u00a0T\u00ednh c\u00e1c t\u00edch ph\u00e2n sau b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ed5i bi\u1ebfn s\u1ed1:<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

B\u00e0i 13 (trang 148 SGK Gi\u1ea3i t\u00edch 12):\u00a0T\u00ednh di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u01b0\u1eddng:<\/strong><\/span><\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

B\u00e0i 14 (trang 148 SGK Gi\u1ea3i t\u00edch 12):\u00a0T\u00ecm th\u1ec3 t\u00edch v\u1eadt th\u1ec3 tr\u00f2n xoay thu \u0111\u01b0\u1ee3c khi quay h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi c\u00e1c \u0111\u01b0\u1eddng y = 2x^{2<\/sup>\u00a0v\u00e0 y = x3<\/sup>\u00a0xung quanh tr\u1ee5c Ox.<\/strong><\/span><\/p>\n}

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

Ta c\u00f3: 2x^{2<\/sup>\u00a0= x3<\/sup> \u21d4 x2<\/sup>\u00a0(2 – x) = 0 \u21d4 x = 0 v\u00e0 x = 2<\/p>\n}

Ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng cong l\u00e0: x = 0 v\u00e0 x =2<\/p>\n

B\u1edfi v\u00ec 2x^{2<\/sup>=x3<\/sup>=x2<\/sup>\u00a0(2-x)\u22650 v\u1edbi x\u22642 n\u00ean \u0111\u01b0\u1eddng cong y=2x2<\/sup>\u00a0n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng cong y=x3<\/sup>\u00a0trong kho\u1ea3ng (0; 2). Do \u0111\u00f3 th\u1ec3 t\u00edch c\u1ea7n t\u00ednh l\u00e0:<\/p>\n}

<\/p>\n

B\u00e0i 15 (trang 148 SGK Gi\u1ea3i t\u00edch 12):\u00a0Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh sau tr\u00ean t\u1eadp s\u1ed1 ph\u1ee9c:<\/strong><\/span><\/p>\n

(3+2i)z-(4+7i)=2-5i<\/strong><\/span><\/p>\n

(7-3i)z+(2+3i)=(5-4i)z<\/strong><\/span><\/p>\n

z^{2<\/sup>-2z+13=0<\/span><\/p>\n}

z^{4<\/sup>-z2<\/sup>-6=0<\/span><\/p>\n}

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

<\/p>\n

B\u00e0i 16 (trang 148 SGK Gi\u1ea3i t\u00edch 12):\u00a0Tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9, h\u00e3y t\u00ecm t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m bi\u1ec3u di\u1ec5n s\u1ed1 ph\u1ee9c z th\u1ecfa m\u00e3n t\u1eebng b\u1ea5t \u0111\u1eb3ng th\u1ee9c:<\/strong><\/span><\/p>\n

a) |z| < 2<\/strong><\/span><\/p>\n

b) |z – i| \u2264 1<\/strong><\/span><\/p>\n

c) |z – 1 – i| < 1<\/strong><\/span><\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a) T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m M(x; y) c\u1ee7a m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 bi\u1ec3u di\u1ec5n s\u1ed1 ph\u1ee9c z = x + yi th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n:<\/p>\n

|z|<2 \u21d4 \u221a(x^{2<\/sup>+y2<\/sup>\u00a0)<2 \u21d4x2<\/sup>+y2<\/sup><4<\/p>\n}

C\u00e1c \u0111i\u1ec3m M(x; y) nh\u01b0 v\u1eady n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m O b\u00e1n k\u00ednh b\u1eb1ng 2 kh\u00f4ng k\u1ec3 c\u00e1c \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n

b) Gi\u1ea3 s\u1eed z=x+yi=>z-i=z+(y-1)i<\/p>\n

|z-1|\u22641 \u21d4 \u221a(x^{2<\/sup>\u00a0(y-1)2<\/sup>\u00a0)\u22641 \u21d4x2<\/sup>+(y-1)2<\/sup>\u22641<\/p>\n}

T\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m bi\u1ec3u di\u1ec5n c\u00e1c s\u1ed1 ph\u1ee9c th\u1ecfa m\u00e3n |z \u2013 1|\u22641 l\u00e0 c\u00e1c \u0111i\u1ec3m c\u1ee7a h\u00ecnh tr\u00f2n t\u00e2m (0; 1) b\u00e1n k\u00ednh b\u1eb1ng 1 k\u1ec3 c\u1ea3 bi\u00ean.<\/p>\n

c) z=x+yi=>z-1-i=(x-1)+(y-1)i<\/p>\n

|z-1-i|<1 \u21d4 (x-1)^{2<\/sup>+(y-1)2<\/sup><1<\/p>\n}

T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m \u0111ang x\u00e9t l\u00e0 c\u00e1c \u0111i\u1ec3m c\u1ee7a h\u00ecnh tr\u00f2n ( kh\u00f4ng k\u1ec3 bi\u00ean) t\u00e2m (1;1), b\u00e1n k\u00ednh b\u1eb1ng 1.<\/p>\n

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 <\/p>\n","protected":false},"excerpt":{"rendered":"

C\u00e2u h\u1ecfi 1 (trang 145 SGK Gi\u1ea3i t\u00edch 12):\u00a0\u0110\u1ecbnh ngh\u0129a s\u1ef1 \u0111\u01a1n \u0111i\u1ec7u ( \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn) c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 tr\u00ean m\u1ed9t kho\u1ea3ng. L\u1eddi gi\u1ea3i: Cho h\u00e0m s\u1ed1 y = f(x) x\u00e1c \u0111\u1ecbnh tr\u00ean K, h\u00e0m s\u1ed1 f(x): \u0110\u1ed3ng bi\u1ebfn ( t\u0103ng) tr\u00ean K n\u1ebfu \u2200 x1, x2\u00a0\u2208 K: x1\u00a0< x2\u00a0=> f(x1) < […]<\/p>\n","protected":false},"author":3,"featured_media":20781,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1298],"tags":[1377,1356,1355],"yoast_head":"\n