kIẾN THỨC CƠ BẢN VỀ hàm số lôgarit

1 N > log a N a a N ( a > 0, a *a>1 : *0[...]... y' 1 2 ln x x Bài 2 : a y x 2 ln y 2 x ln x2 1 x 2 1 y ' 2 x.ln x 2 x2 x 2 x2 1 1 2 2 x.ln x 1 x3 2 x2 1 b log 2 x 2 x 1 y log 2 x 2 c y y 3 3 x 1 ln 2 x y' x 4 x 4 log 2 log y' 2 3 ' 1 3 2 ln x 3 1 x 2 3 x 3 ln x 1 ln 2 16 x 4 2 : x 4 x 4 16 x 4 ln 2 2 x2 9 x 5 x2 9 x 5 log 3 1 f y log y ln x x 4 x 4 e y log 3 y 2 ln 2 x d y log 2 y 2x 1 x x 1 ln 2 y' y' 2 1 2x x 5 x 2 ln 3 x 5 9 x2 9 : x 5 x 2 10... cos5x x2 1 cos5x x2 5x 2 lim 2 x 0 4 5x 25 2 Bài 3 a lim x 0 cosx cos3x sin 2 x 2 sin 2 25 2 1 cosx cos3 x lim x 0 sin 2 x lim x 2 lim x 2 sin 2 x 0 x 2 2 sin 2 x t 2 tan t t 2 sin cos 2 2 c xlim x 2 sin 2 t 2 1 cosx t Khi x cos ;t 2 0 2 2 t 2 lim x x 1 x t ;t 1 sin t t 1 t anx cosx lim t 0 2 t 1 cost sint cot t tan t 2 t 2 0 3 x 2 x sin x 4 1 2 3t t lim x 2 sin 6t 3 x 3 x lim 6t 3 t 0 4 x 4 tan 2 2 cos... lim x 1 t anx= 3 x 3 lim x 2 sin x x lim 4 1 t anx cosx t x 4 cos x.sin 2 x lim x 0 sin 2 x x 1 t anx cosx b lim x 2 sin 2 x sin 2 2 cos x sin x x 4 x 4 sin x 2 2 cos x sin x 4 4 ;t 0 2 2 cos 2 lim o t 2 2 t 2 1 cost+sint sint 4 t t t 2 sin cos 2 2 2 t t 2 sin cos 2 2 2 tan 4 sin t 2 sin 2 t 4 ;x 2 2 cos x 4 2 1 cost+sint sint lim t t 2 sin 2 t t cos 2 2 t cos 2 2 tan t 2 2 3 ... 1 e log 1 2 2 1 1 2 0 Ta có : log 1 e e log 1 2 2 -GA-RÍT Bài 1 x2 2x 2 ex a y x2 y 2 x 2 ex s inx-cosx e 2 x c y y 2 x 2 ex x2 2 x 2 ex y' cosx+sinx e 2 x ex ex ex ex e e e e y x y' x ex e x ex e e x ex e x x 2 y' 2x x 2 1 ln x x ln x x 3sin x c osx e 2 x x ln x 2 1 e y 2 s inx-cosx e 2 x x d y ln x 2 1 y x2 e x s inx-cosx e 2 x b y y y' y' 1 1 x ln x x2 x 1 ln x x2 e x ex e x 4 e x e x 2 f y 1 ln... ln 2 ln e3 Ta có : 1 8 ln e 2. 3 6 8 ln 8 1 9 1 e 2 ln e3 Bài 3 a/ log 1 3 log 3 2 1 2 2 1 Ta có : log 1 3 log 3 2 log 3 40 8 5 log6 2 1 Ta có : 6 8 9 1 2 0 1 2 log 3 log 3 1 2 1 2 1 1 log 3 2 1 2 1 log 3 2 2 * log 3 1 2 1 1 log 3 2 2 3 18 5 b/ 4log 7 7log 4 5 5 Ta có : 4log 7 log5 7 7log7 4 5 7log5 7.log 7 4 7log5 4 c/ log 3 7 log 7 3 2 Ta có : log 3 7 0 d/ 3log 2 5 1 log 3 7 5log5 3 2 1 log 3 2 log... lim x lim 4 x 0 lim x x 0 e5 x 3 2 ln 4 x 1 ln 4 x 1 d lim x 0 x sin 2 x 3x ln 2 x 1 tan x ex 1 0 x lim x x 1 1 1 .2 ln 2 x 1 0 2 x 2 lim ln 3 x 1 lim x ln 3 x 1 0 3 x 3 lim 2 3 2 1 2x ln 2 x 1 lim x 0 tan x b lim x 0 lim x e2 x 0 c lim x 0 e2 x lim x 0 ln 2 x 1 2x tan x x x 2 e3 x 5x e3 x 5x e2 x 1 e3 x 1 lim 3 0 5 x 0 5 3x 2 x 2 lim x 2 3 5 5 1 5 e3 x 1 x e3 x 1 e3 x 1 lim 3 3 0 x 0 x 3x lim x d lim... log 3 7 0 d/ 3log 2 5 1 log 3 7 5log5 3 2 1 log 3 2 log 2 5 5log 2 5.log 5 3 5log2 3 log19 log 2 1 log 3 log 10 log 3 log 3 10 2 Ta có : 19 361 log19 log 2 log log 2 4 log 900 f/ log 5 361 4 log 7 5 log 900 1 log 3 log19 log 2 2 log 5 log 7 2 2 Ta có : 2 5 log2 3 Ta có : 3log 5 e/ log 3 7 log 7 3 log 3 7 7 5 7 2 log 5 7 2 log 5 7 log 5 log 7 2 Bài 4 Hãy so sánh : a log 3 6 5 log 3 5 6 6 5 Ta có :... 2 log 1 h/ 9 9 8 9 5 log 3 2 log 1 Ta có : 9 k/ 9 log6 2 1 6 1 log 2 6 3 2 log 3 2 log 9 8 9 3 log 3 2 log 3 8 9 log 3 2. 3 3 6 8 8 36 8 3 1 log 2 18 6 5 6 log6 2 log6 5 6 log6 10 6 log6 1 10 1 10 3 1 1000 Bài 2 Hãy so sánh : a/ log 2 10 log 5 30 Ta có : log 2 10 log 2 8 3 log 2 10 log 5 30 log 5 30 log 5 36 3 b/ log 3 5 log 7 4 Ta có : log 3 5 log 3 3 1 log 7 4 log 7 7 1 log 3 5 log 7 4 1 e c/ 2. .. x 2 10 x 9 x 5 x 2 9 ln 3 x 2 x 1 x 2 x y' x 1 1 1 x : ln10 16 x x 2 x x 1 8 x ln10 1 x Bài 1 a lim x 0 lim x ln 3 x 1 ln 2 x 1 x ln 3 x 1 ln 2 x 1 x 0 b lim x 0 x ln 3 x 1 3x lim x 0 sin 2 x 2x 2x ln 3 x 1 0 sin 2 x c lim x 0 lim x lim x e 0 e5 x x 3 0 4x 0 4 2x 3 e3 3 lim e 5 x 0 e5 x 1 2 5 x 5e 3 2 ex 1 x 1 1 ex 1 x 1 1 a lim x 0 ln 4 x 1 e3 2x lim x lim 4 x 0 lim x x 0 e5 x 3 2 ln 4 x 1 ln 4 x ... log log 11 log 2log log f/ Ta có : log log log 25 log log 2 25 g/ log2 log4 Ta có : 11 25 92 625 81 648 81 2log log 25 2 log 25 2log log 8 18 log log 11 81.11 2log 891 5 log 2 11 90 log log... log 2 sin b B log B log 3 log cos 12 log cos 12 3 log 2 sin 12 49 21 49 21 log log 12 12 cos log sin 12 log10 tan log10 cot d D log x D log tan 4.cot log log1 log 21 6 log 10 log 3 log 21 6 2log... logx logx logx 20 11 logx 1 .2. 3 20 11 log 20 11! 20 11! a b2 a c2; a a2 log c b a 0, c 0, c b , : log c b a log c b a log c b a.log c b a 0, b c2 b2 log c b a c b c b 2 log c b a.log c b a log a