B\u00e0i 42 (trang 97 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

T\u00ecm sai l\u1ea7m trong l\u1eadp lu\u1eadn sau:<\/p>\n

Ta c\u00f3 ln e^{2<\/sup>=2lne = 2.1 = 2 v\u00e0 ln(2e) = lne + lne = 1+ 1 = 2<\/p>\n}

T\u1eeb \u0111\u00f3 suy ra e^{2<\/sup>=2e m\u00e0 e \u2260 0 n\u00ean e = 2!<\/p>\n}

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

L\u1eadp lu\u1eadn tr\u00ean sai l\u1ea7m ch\u1ed7 ln(2e) = lne +lne<\/p>\n

L\u1eadp lu\u1eadn \u0111\u00fang l\u00e0: ln(2e) = ln2 +lne<\/p>\n

B\u00e0i 43 (trang 97 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

Bi\u1ec3u di\u1ec5n c\u00e1c s\u1ed1 sau \u0111\u00e2y theo a = ln2; b = ln5.<\/p>\n

<\/p>\n

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

ln500 = ln125.4 = ln5^{3<\/sup>+ln\u206122<\/sup>\u00a0= 3ln5+2ln2=3b+2a<\/p>\n}

ln\u2061(16\/25)=ln16-ln25=ln2^{4<\/sup>-ln\u2061(52<\/sup>)=4ln2-2ln5=4a-2b<\/p>\n}

ln\u20616,25=ln\u2061(625\/100)=ln625-ln100=ln\u2061(5^{4<\/sup>)-ln\u206125.4=4ln\u20615 – 2ln\u20615-2ln2=2ln5-2ln2=2b-2a<\/p>\n}

<\/p>\n

B\u00e0i 44 (trang 97 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

Ch\u1ee9ng minh:<\/p>\n

<\/p>\n

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

Ta bi\u1ebfn \u0111\u1ed5i v\u1ebf tr\u00e1i:<\/p>\n

<\/p>\n

B\u00e0i 45 (trang 97 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

S\u1ef1 t\u0103ng tr\u01b0\u1edfng c\u1ee7a m\u1ed9t lo\u1ea1i vi khu\u1ea9n theo c\u00f4ng th\u1ee9c S=A.e^{tr<\/sup>, trong \u0111\u00f3 A l\u00e0 s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n ban \u0111\u1ea7u, r l\u00e0 t\u1ec9 l\u1ec7 t\u0103ng tr\u01b0\u1edfng (r > 0), ti l\u00e0 th\u1eddi gian t\u0103ng tr\u01b0\u1edfng. bi\u1ebft s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n ban \u0111\u1ea7u l\u00e0 100 con v\u00e0 sau 5 gi\u1edd c\u00f3 300 con. H\u1ecfi sau 10 gi\u1edd c\u00f3 bao nhi\u00eau c\u1ee7a vi khu\u1ea9n. Sau bao l\u00e2u s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n ban \u0111\u1ea7u s\u1ebd t\u0103ng g\u1ea5p \u0111\u00f4i.<\/strong><\/em><\/p>\n}

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

Sau 5 gi\u1edd, t\u1eeb c\u00f4ng th\u1ee9c S=A.e^{rt<\/sup>\u00a0ta c\u00f3 300 = 100.e5r<\/sup>\u00a0=> 3=e5r<\/sup><\/p>\n}

<\/p>\n

Sau 10 gi\u1edd s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n l\u00e0<\/p>\n

<\/p>\n

=> S=100.e^{2ln3<\/sup>=100.(eln\u20613<\/sup>\u00a0)2<\/sup>=100.32<\/sup>=100.9=900 (con)<\/p>\n}

\u0110\u1ec3 s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n t\u0103ng l\u00ean g\u1ea5p \u0111\u00f4i th\u00ec:<\/p>\n

<\/p>\n

=> t=3 gi\u1edd 9 ph\u00fat.<\/p>\n

B\u00e0i 46 (trang 97 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

Cho bi\u1ebft chu k\u00ec b\u00e1n h\u1ee7y c\u1ee7a ch\u1ea5t ph\u00f3ng x\u1ea1 Plutanium Pu^{239<\/sup>\u00a0l\u00e0 24360 n\u0103m (t\u1ee9c l\u00e0 m\u1ed9t l\u01b0\u1ee3ng Pu239<\/sup>\u00a0sau 24360 n\u0103m ph\u00e2n h\u1ee7y ch\u1ec9 c\u00f2n l\u1ea1i m\u1ed9t n\u1eeda). s\u1ef1 ph\u00e2n h\u1ee7y \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c S=A.ert<\/sup>, trong \u0111\u00f3, A l\u00e0 l\u01b0\u1ee3ng ch\u1ea5t ph\u00f3ng x\u1ea1 ban \u0111\u1ea7u, t l\u00e0 t\u1ec9 l\u1ec7 ph\u00e2n h\u1ee7y h\u00e0ng n\u0103m (r < 0), t l\u00e0 th\u1eddi gian ph\u00e2n h\u1ee7y, s l\u00e0 l\u01b0\u1ee3ng c\u00f2n l\u1ea1i ph\u00e2n h\u1ee7y sau th\u1eddi gian ph\u00e2n h\u1ee7y t. H\u1ecfi sau 10 gam Pu239<\/sup>sau bao nhi\u00eau n\u0103m s\u1ebd ph\u00e2n h\u1ee7y c\u00f2n l\u1ea1i 1 gam.<\/strong><\/em><\/p>\n}

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

T\u00ednh t\u1ec9 l\u1ec7 ph\u00e2n h\u1ee7y h\u00e0ng n\u0103m:<\/p>\n

Ta c\u00f3:<\/p>\n

<\/p>\n

G\u1ecdi t_{0<\/sub>\u00a0l\u00e0 th\u1eddi gian m\u00e0 10gam Pi^{239<\/sup>\u00a0ph\u00e2n h\u1ee7y c\u00f2n 1 gam ta c\u00f3:<\/p>\n}}

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

B\u00e0i 42 (trang 97 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):\u00a0 T\u00ecm sai l\u1ea7m trong l\u1eadp lu\u1eadn sau: Ta c\u00f3 ln e2=2lne = 2.1 = 2 v\u00e0 ln(2e) = lne + lne = 1+ 1 = 2 T\u1eeb \u0111\u00f3 suy ra e2=2e m\u00e0 e \u2260 0 n\u00ean e = 2! L\u1eddi gi\u1ea3i: L\u1eadp lu\u1eadn tr\u00ean sai […]<\/p>\n","protected":false},"author":3,"featured_media":23498,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\n