Hướng dẫn ôn tập chương II Giải tích 12 nâng cao25630

H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Biên so n: GV Lê V n Hi p- 0985769905 Tr ng THPT Sóc S n – Hịn t – Kiên Giang M – LƠGARIT, PT M – LÔGATRIT, BPT M - LÔGARIT  2x 3x  Bài 1: Tìm t p xác đ nh c a hàm s sau: a) y  log0,5 b) log 3x  2x d) y  log (3x  x  2) e) y  log (2  5x  2x ) c) y = log3 (3  7x) 3 Bài 2: Tìm t p xác đ nh c a hàm s sau: a) y = (x2 – x – 6)-3 c) y   2x  5x  3 2 d) y   8x  2x 4   b) y = (2x – 4x2)0 e) y   12x     f) y   10x  3x   Bài 3: Tính đ o hàm hàm s sau: a) y =  sin x   ln x  c) y = (e2x  1)  log2 (2x  1) d) y = (3x – 2).ln2x e) f(x) = 2x.ex + 3sin2x Bài 4: Tính đ o hàm hàm s sau: a) f(x) = 5x2 – 2x.cosx d) f(x) = b) y = e) y =  3cos2 x  ln x  5x   ln(sin x) c) y  log (x3  cos x) h) f(x)  d) y  ln(2x  1) 3x  3x f) y =  3   ln e2x   log3 x  log(cos x) lg x c) f(x) = e x  x f) f(x) = log32 (2x  1)  e3x    x3 i) y  ln3 5x 1 x Bài 5: Tính đ o hàm hàm s sau: a) y  ex ln(cos x) g) y  (sin3x  ex )2  b) f(x) = 2x3   j) f(x)  esin2x  cos4 [ln2 (sin 2x)] b) f(x)  (2x  1)ln(3x2  x) e) y  ln(x   x2 ) f) y  (3x2  2).ln3 2x 2x  ln(x2  1) h) y  x2 ln i) y  j) y  x2 e4x  g) y   x3 ln x5 1 x x3 Bài 6: Ch ng minh r ng hàm s cho th a mãn h th c đ c ch ra: a) y = ex cos x , ta có: 2y  2y  y  b) y = (x + 1)ex, ta có: y  y  ex c) y  e 4x  2e x , ta có: y   13y   12y  d) y = ex.sinx, ta có: 2y  2y  y  e) y  xe  x2 , ta có: xy  (1  x2 )y f) y  e2x sin 5x , ta có: y  4y  29y  g) y  x2 ex , ta có: y  2y  y  ex h) y  esin x , ta có: y cosx  ysin x  y  Bài 7: Tìm GTLN GTNN c a hàm s sau: a) f (x)   e2x  5e x  4x  đo n [-1; 1] ex b) y = x2ex đo n [-1; 1] c) y = (x2 – 3)ex đo n [0; 2] d) y = đo n [0; 2] 2x   7 e) f(x)  e2x  4ex  đo n [0; ln4] f) y  e2x  x2  x   [-2; 0] 2  Bài 8: Tìm GTLN GTNN c a hàm s sau: a) y = x2 – ln(1 – 2x) đo n [-2; 0] b) y  x  ln(2  x) đo n [-2; ] 2 ln x 1 c) y = xlnx đo n [ ; 2] d) y  [1; e3] e) y = x  ln x đo n [1; 4] x x f) f(x) = x2 ln x  đo n [ ; 3] g) f(x) = ln3 x  3ln x  đo n [e; e3] 2 x h) y  ln(x  x  2) [3; 6] i) y  ln x.ln(e7 x).ln [ e5 ;e ] e ThuVienDeThi.com H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Bài 9: Gi i ph 1 d)   7 ng trình sau: a) 3x x  2x 3 7 e) 1,5  x 1 2 5x  5x  Biên so n: GV Lê V n Hi p- 0985769905 Tr ng THPT Sóc S n – Hịn t – Kiên Giang 9 2   3 b) 5x x 1 5 f)   3   Bài 10: Gi i PT sau: a) 28x 58x  0,001 105 1 x x5 x 1 5x 6      25  1 c) 2x  4x 1 x  x 1 g) 0,125.161x  1 b) 32x1.153x.53x  x 17 3x 8 32 c) 5x1  10x.2 x.5x1 x 1 e) 32 x 7  0,25.125 x 3 f) 5x.8 x  500 g) 2x 3x  216 d) 4x1.3x3.5x1  9600000 Bài 11: Gi i ph ng trình sau: a) 3x 1  3x 2  3x 3  3x 4  2250 b) 3x 1  3x  3x 1  9477 d) 5x1  6.5x  3.5x1  52 e) 3x1  6x.22.3x1 c) 2.3x1  6.3x1  3x  f) 3x  3x 1  3x 2  2x  2x 1  2x 2 g) 52x 1  3x 1  52x  3x h) 5x  5x1  5x2  3x  3x1  3x3 b) 32x 2  4.3x 2  27  c) 3.52x1  2.5x 1  0,2 Bài 12: Gi i PT sau: a) 64x  8x  56  d) 4x 2  2x 5   e) 22x 3  3.2x 2   f) 9x – – 36.3x – + = g) 22x 1  33.2x 1   h) 322x  2.32x  27  i) 212x  15.2x   j) 32x8  4.3x5  27  k) 22x6  6.2x7  17  l) 32x5  36.3x1   b) 5x  53x  20  c) 31 x  31x  10 Bài 13: Gi i PT sau: a) + 7 x = 71 + x d) 4x   2x  21x e) 2x2  22x  15  f) 32x  32x  30 g) 4x  234x  h) 7x  2.71x  i) 3.9x  2.9 x   j) 5x  251x  k) 5x1  52x  27  2 2 Bài 14: Gi i ph ng trình sau: a) 9x 1  36.3x 3   b) 9x 1  3x 1   2 2 2 2 e) 4x 2  9.2x 2   f) 32x 2x1  28.3x x   c) 4x 1  3.2x 2   d) 51 x  51x  24 2 2 2 g) x2  16  10.2 x2 h) 2x x  22xx  i) 41 x  41x  15 j) 101 x  101x  99 2 k) 9x 1  36.3x 3   l) x  51 x   m) 432cosx  7.41cosx   x x x Bài 15: Gi i ph ng trình sau: a) 2.49 – 9.14 + 7.4 = b) 5.25x + 3.10x – 2.4x = d) 6.9x  13.6x  6.4x  e) 25x  10x  22x1 f) 3.16x  2.81x  5.36 x c) 4.9x  12x  3.16x  x  x  x x x x x x g)  18  2.27 h)   i) 6.9  13.6  6.4  j) 2.4   Bài 16: Gi i ph ng trình sau: a) e2x – 3ex + = b) e2x – 3ex – + 12e-x = d) ln2x – lnx – = d) ln3x – 3ln2x – 4lnx + 12 = c) e6x  3.e3x   x x x 2x  6.(0, 7) x  c) x 100  d) x2 2x  x   7.3 ng trình sau: a)  Bài 18: Gi i ph   x 1  x  x ng trình sau: a)       12 3  3 Bài 17: Gi i ph c)  3 2  x 2   x  x b) 4x  x2 2x x 1   2  3 d)  2 x e) 4x 6   16   ng trình sau: a) log x  log x  log Bài 19: Gi i ph x x  x 5 x2   12.2x 1  5.2x1   x x 5 x2  b)  21   21  2x 3 e)  5   x  8  6   x  x 3 52   10 x b) log x.log3 x.log9 x  11 11 d) log5 x  3log 25 x  log 125 x  e) log3 x  log9 3x  log 27 x  2 Bài 20: Gi i ph ng trình sau: a) log (x  5)  log (x  2)  b) log (x  1)   log x c) log (x  3)  log (x  1)   log16 64 d) 2log(x  2)  log(3x  6)  log e) log (x  2)  log x c) log x  log x  log8 x  g) log25 (3x  11)  log5 (x  27)   log5 f) log2 (x  3)  log  log (x  1)  log2 (x  1) ThuVienDeThi.com H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Biên so n: GV Lê V n Hi p- 0985769905 Tr ng THPT Sóc S n – Hòn t – Kiên Giang ng trình sau: a) log3 (2x  1)  log (5  x)  2 Bài 21: Gi i ph c) log2 x  log4 (x  3)  b) log2 (x2  1)  log (x  1)  e) log3 (x  2)  log3 (x  4)2  d) log4 (x  3)  log2 x    log4 f) log5 (x  1)  log  log (x  2)  log (x  2) g) log2 (x  2)  log 3x   25 x5 j) log4 (log2 x)  log2 (log4 x)   log2 (x2  25)  x5 1 1 x2 k)  log(2x  1)  log(x  9) l) log2 (x  2)   log 3x  m) log4  log2 (4x)2  10  2 16 Bài 22: Gi i ph ng trình sau: a) ln(x + 1) + ln(x + 3) = ln(x + 7) b) ln(4x + 2) – ln(x – 1) = lnx c) log(x2  2x  3)  log(x  3)  log(x  1) d) lg(x  6)  lg(2x  3)   lg 25 b) 4log 24 x   2log x c) 3log82 x  log2 x   Bài 23: Gi i PT sau: a) log x  log 22 x  h) log9 (x  8)  log3 (x  26)   d) 2(log7 x)2  3log7 x   i) log2 e) log2 4x  log2 x2 8 f) log2 x  3log2 x  log x  2 h) log25 x  log5 (5x)   g) log21 x  log4 x   i) 4log9 x  log x  k) log22 (2  x)  8log (2  x)  j) log24 x  log4 x2   l) log32 x   m) log25 x  log25 5x   Bài 24: Gi i PT sau: a) c) logx  log4 x  0 n) log2 x3  20 log x   log x  3log 27 x  2log3 x d) log5 x   logx x g) log3 (4.3x1  1)  2x  j) log2 (5x1  25x )  b) log5 x  logx x 9 f) log3 (3x1  26)   x 1 l) log (6x 1  36x )  2 ng trình sau: a) log (2  1).log (2 i) 16 x 1 x 10 x 10 m) log3 (3x  8)   x b) log3 (3x  1).log3 (3x 1  3)   2)  d) log3 (3x  1).log3 (3x1  3)  12 f) log2 (4.3x  6)  log2 (9x  6)  ng trình sau: a) x 2x 1 h)    x 1 9 i) log4 (3.2x1  5)  x x 1 e)   2 x e) log3 (9x  9)  x  log3 (2.3x  8) c) (x  1) log5  log(3x 1  3)  log5 (11.3x  9) 1 d)   5 f) log 2  log2 4x  c) log (9  2x )  5log5 (3x) h) log2 (12  2x )   x e) x log x 27.log9 x  x  c) log2 (2x)2 log2x  b) log7 (6  )   x k) log (5x 1  25x )  2 Bài 27: Gi i b t ph 2 e) logx2  log9 x  Bài 26: Gi i ph log2 x  log x   4 x Bài 25: Gi i PT sau: a) log3 (3  8)   x d) log2 (4.3x  6)  log2 (9x  6)  o) log3 (9x) x  2x  24 4x 15x 13 3x  2  0,125.8 x5 x 15 1 7 b)   9 1 f)   7 1 j)   3 2x 3x  c) 32x 9x 8x  9x2 17x 1 ThuVienDeThi.com g) log2 (3x  3)  log3x 3   7x 1   3 2  5x 3x  g)  x  6x    2 5x 25  k)   5 H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Biên so n: GV Lê V n Hi p- 0985769905 Tr ng THPT Sóc S n – Hịn t – Kiên Giang Bài 28: Gi i b t ph ng trình sau: a) 4x  3.2x   b) 16x  4x   c) 52x  3.5x  d) 9x – 2.3x < e) 4 x0,5  7.2 x   f) 4.4x  2x   g) 52x3  2.5x2  h) 52x1  5x  i) 2.9x2  5.3x1  133 j) 5.72x1  2.7x2  6517  k) 32x8  4.3x5  27 b) 3x  3 x2   c) 2x  23x  Bài 29: Gi i b t PT sau: a) 2x  2 x   d) 3x  31x   e) 3.5 x  5x2  10 f) 2.7x2  3.74x   g) 2.5x1  4.52x  70 Bài 30: Gi i b t PT sau: a) x  2x 1    3 2x  x b) 3 x 1 x 2 2 x 3  1 x 3x 1 1 e)       12 f) d) 3.9  21.3 6 3 3 b) 27x  12x  2.8x Bài 31: Gi i b t PT sau: a) 2.14x  3.49x  4x  x  2x  x x 2x  x 1 2    2 2 x 9 x 1 1 1       128  4 8 c) 4x  2.52x  10x  d) 5.4x  2.52x  7.10x d) 9.4 x  5.6 x  4.9 x Bài 32: Gi i b t PT sau: a) log (x  5x  6)  1 c) 1 x 1 e) 9.25x  16.15 x  25.9 x b) log8 (4  2x)  c) log5 (3x  5)  2 d) log (2x  3)  log (3x  1) f) log3 (5x2  6x  1)  e) log (x  4x  5)  g) log3 (4x  3)  log (2x  3)  h) log (x2  6x  8)  log5 (x  4)  j) log (x2  6x  5)  log3 (2  x)  i) log0,1 (x2  x  2)  log0,1 (x  3) k) log x  l) log 1 2x  3x   log  x  1  2 c) log22 x  8log x   1  log x  log x 1  1  log x log x x  3x  0 x d) log22 x  3log2 x   e) log 21 x  6log x   f) log 21 x  log x  n)  x2  x   2x   b) log 0,7  log   c) log  log 0  x x      2 ng trình sau: a) log5 x  log5 x   b) log3 x  5log3 x   Bài 33: Gi i b t PT sau: a) log Bài 34: Gi i b t ph m) log x  2 x  log 0,5 x   g) log 0,5 h) 2log5 x  log x 125  Bài 35: Gi i b t PT sau: a) log (3x  1).log 3x   16 c) log5 (4x  144)  4log5   log5 (2x 2  1) b) log3 (3x  1).log (3x   9)  3 d) log (7.10x  5.25x )  2x  x y x y   x  y  3.2  2.3  2, 75 3  1152 Bài 36: Gi i h PT sau: a)  x y b)  2x c)  2y   4   0,5 2   0, 75 log (x  y)  x  y2  log x  log 7.log y   log  x  y  20 d)  e)  f)  log x  log y   log 3  log y  log 5(1  3log x) log (x  y)  log (x  y)  Bài 37: Gi i ph x 3 b)    x  5 5 x ng trình sau: a)   6 x x c) + = d)   c)   2x Bài 38: Gi i ph ng trình sau: a) 9x + 2(x – 2).3x + 2x – = b) 25x – 2(3 – x).5x + 2x – = c) log22 x  (x  1) log x  2x   d) 3.4x  (3x  10).2x   x  x x x x x ThuVienDeThi.com ...H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Bài 9: Gi i ph 1 d)   7 ng trình sau: a) 3x x... log5 f) log2 (x  3)  log  log (x  1)  log2 (x  1) ThuVienDeThi.com H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Biên so n: GV Lê V n Hi p- 0985769905 Tr ng THPT Sóc...  7x 1   3 2  5x 3x  g)  x  6x    2 5x 25  k)   5 H ng d n ôn t p ch ng II Gi i tích 12 nâng cao n m h c 2015 - 2016 Biên so n: GV Lê V n Hi p- 0985769905 Tr ng THPT Sóc