bài tâp hình và 100 đề thi học kì 2 có đáp án đầy đủ

   a !   "!!!#$%&'()*$++,% (/0(1& 2" ∆ ABC  "3+&%/4+5 ⊥ ⊥ ,SA BC SB AC 63+&%/4+5 ( ) ⊥ SH ABC  7++%8").&9(:+;<   !"!#$! ⊥ % ⊥ #$ ⊥ ! &' ⊥ !   SN BC BC SH AH BC ⊥  ⇒ ⊥  ⊥  &' ⊥ !% ()*!$ ( ) ⊥SH ABC +,- .!/0-123+   ( ) HS ABC⊥ #$%-4--5!623 !$ .!/0-123 .%! ( ) 7 7 7 8#   7 b AH b SAH a SA a = = =  9:$ .!/0-123(;  8  α  #8-8 7 8#  b a α = = >?#@A (%(1&BC"! ( ) ⊥ SA ABCD ! "! · = ° 120BAD  "7DE#+2"?). 6,% (/*+#%F&2"3+&%/4+5 ( ) ⊥ OH ABCD  7DE#2"+).? 94<-4--8#$ AC BD⊥ ( ) SA ABCD⊥ ⇒ -4--5!62<3 !$ .-=(;>? ? ( @%A(4-B!#$%@!  ( ) ( ) SA ABCD OH ABCD ⊥ ⇒ ⊥ <#$ .!< .! (;CD ? 4B!BE*F   · = °30BAC  = = = = SA SB SC SD a  !"#$% ( ) ⊥ SO ABCD  &'(")*+ ,-"./012#"34!"#$% ( ) ⊥MN SBD  5'(67") 94@8<G!"!"!"!<6 ( ) SO AC SO ABCD SO BD ⊥  ⇒ ⊥  ⊥  (  ( ) SO ABCD⊥ #$@-4--5!62<3 4 · ? 7?BCA = #$B<BH#$ 7  a CO = · ( ) · ? 7 8# 7?  OC SCO SCO SC = = ⇒ = +9:$ .!2<3(;7? ?    ( ) ( ) ( ) ( ) SO ABCD SO BD BD SO BD SAB DB AC BD SAB MN SAB MN AC ⊥ ⇒ ⊥ ⊥  ⇒ ⊥  ⊥  ⊥   ⇒ ⊥    P I%-4--5@6!   ( ) AC SBD AC HO⊥ ⇒ ⊥ +J8F-1@%8F E -!  B!@BE*F@#$@%"  a 8 ∆ABC "19:194" :; · = °120BAC <"=> = 3SA a ,"?"@ 4A: !"#$% ( ) ⊥ AK SBC  &'(")"=>%*+*+ '(67")   ( ) SA ABC SA BC⊥ ⇒ ⊥ %A8#$ AH BC⊥ ( ) ( ) ( ) AH BC BC SAH SA BC BC SAH BC AK AK SAH ⊥  ⇒ ⊥  ⊥  ⊥   ⇒ ⊥  ⊂   K-4--56!%#$ AK SH⊥ ( ) AK SH BC AK AK SBC BC SH H ⊥   ⊥ ⇒ ⊥   ∩ =  ( ( ) ( ) ( ) ( ) ( ) ( ) · ( ) · ( ) ·    AH ACB SH SBC ABC SBC SH AH AHS SBC ABC BC SH AH BC ⊂   ⊂  ⇒ = =  ∩ =   ⊥  ?  7 L? SA H H AH = = ⇒ =  %8FE -!:$M.!(; G>?#@A? (%C"!+ · = °60BAD ! = 3 2 a SA %H*2" -I&9(:+;?<(/J+)K%(/,+(1&2" ∆ ABD  "3+&%/4+5 ( ) ⊥ BD SAC 7! 6,% α  +2";?<).;?<7 α tan 7LM+@+%8"?). 94%-4--5!62<3#$!% ⊥ < <-4--8#$ ⊥ < ( ) SH BD AC BD BD SAC SH AC H ⊥   ⊥ ⇒ ⊥   ∩ =  <-4--8F-  · ? L?BAD = 6B< BHF-+ 7 7 G L  a a OH OA OC= = =                  7  7  7 7 D +  7  7  C 7  D  D C D  7  7 7  a a a a a a SH SA AH AO SH a a a a SC SH HC AO a SC         = − = − = − = − =  ÷  ÷  ÷  ÷  ÷  ÷  ÷         ⇒ =   = + = + = +  ÷   ⇒ = (  ( ) ( ) ( ) ( ) ( ) · ( )  D L  + D  7 SAC BD SAC ABCD AC OH SO SAC SBD SO SH a HO a α α ⊥   ∩ = ⇒ =   ∩ =  = = = N>#@A  ∆ ABC #O*C="! ( ) ⊥SA ABC ! ",% (/*+#%F&2" "3+&%/4+5 ( ) ⊥BC SAI 67LM+@(P#H&9(:+;< 7++%8""%&9(:+;<).;<   ( ) SA ABC SA BC⊥ ⇒ ⊥ 23 BHN6N ⊥ 23 )2323#$ ⊥ 2!N3 (%-4--562!3   ( ) ( ) ( ) ( ) SBC SAI H SI SBC SAI SI ⊥   ⇒ ∈  ∩   OPBE!N Q          C 7 7  a AH AH AI SA AH a = + ⇒ = ⇒ =  Q ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) · ( ) · ( ) ¶ ¶ ( ) ¶ ?   7  7? 7 7   BC SAI ABC ABC BC SBC ABC SI AI SIA SBC SAI SI ABC SAI AI SA a SIA SIA AI a ⊥   ∩ =  ⇒ = =  ∩ =   ∩ =  = = = ⇒ = Q>! ( ) ⊥ SA ABC ! ∆ABC #O*,% %H*2"-I! %H*2"-I ). = =2 3, 2SA a AB a  "3+&%/4+5 ( ) ⊥ AH SBC  67++%8""%&9(:+5;<).;< 7LM+@+%8").   ( ) SA ABC SA BC⊥ ⇒ ⊥ 23 BHN6N ⊥ 23 )2323#$ ⊥ 2!N3 ( ) ( ) BC SAI SA AH AH SAI ⊥   ⇒ ⊥  ⊂    7a %-4--56!N6 AH SI ⊥ ( ) SA AH SI AH AH SBC SI BC I ⊥   ⊥ ⇒ ⊥   ∩ =  ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) · ( ) · ( ) ¶ ¶ ( ) ¶  7   G   7   BC SAI ABC ABC BC SA a SBC ABC SI AI SIA SIA SIA AI SBC SAI SI a ABC SAI AI α ⊥   ∩ =  ⇒ = = = = = ⇒ =  ∩ =   ∩ =  8 α #8-8 α" M-8RB-.!SI8FN"  7a RST UV*+52T?3 1*T52?34BU-F#Q 3 x x x x 3 2 1 2 3 1 lim 1 →− + − + (3 ( ) x x x x 2 lim 1 →+∞ + + − 1*=52?3OP,-6V-#W#F x 0 2= Q x khi x f x x x khi x 2( 2) 2 ( ) ² 3 2 2 2  −  ≠ =  − +  =  1*W52?3,-F8-B-#W#Q 3 x y x 2 2 1 2 − = −  (3 y x 2 cos 1 2= − 1*X527?3-8-4-- 0XBH!+< F-B$(;aA8!@" a 3 +N !@+ 3,-M-8RB-)N5/0-12!<3+ (3,- .B/0-12!32!<3+ 3,-M-8RB-.-A-1!<+ UV/%I+ 1. Theo chương trình Chuẩn 1*G"52?3-X-;0-&4-Q x x 5 3 1− =  ,-YS-Z-S(G)+ 1*N"52?3 3-8-#W y xcot2 = +-X-;Q y y 2 2 2 0 ′ + + = + (3-8-!W x y x 3 1 1 + = −  [-\23+950-&4-50$523F2G]T3+ 2. Theo chương trình Nâng cao 1*G652?3-X-;0-&4-Q x x 17 11 1 = +  -Z+ 1*N652?3 3-8-#W x y x 3 4 − = + +-X-;Q y y y 2 2 ( 1) ′ ′′ = − + (3-8-#W x y x 3 1 1 + = −  [-\23+950-&4-50$523(550$5E U A-1IQ x y2 2 5 0+ − = + RYUYRSZ[\]Z^_]=`T`^=`TT BYabUTT^RSQ 1* c '%d*+ R%F& T 3 x x x x x x x x x 3 2 2 1 1 2 3 1 ( 1)(2 1) lim lim 1 1 →− →− + − + + − = + + ?D?  x x x 2 1 lim (2 1) 0 →− = + − = ?D? (3 ( ) x x x x x x x x x 2 2 1 lim 1 lim 1 →+∞ →+∞ + + + − = + + + ?D? 2 1 1 1 lim 2 1 1 1 1 x x x x →+∞ + = = + + + ?D? = x x x x f x x x x 2 2 2 2( 2) 2 lim ( ) lim lim 2 ( 1)( 2) 1 → → → − = = = − − − 23 ?D? f23" 23 ?D )2323#$f2x36VFx" ?D W 3 x x x y y x x 2 2 2 2 1 2 8 1 ' 2 ( 2) − − + = ⇒ = − − ?D? (3 2 2 2 2 sin 1 2 cos 1 2 ' 1 2 x x y x y x − = − ⇒ = − ?D? X ?D 3 *<+ !+<-4-- 0XBH6 Q@⊥<!⊥<⇒<⊥2!@3 9^@K⊥!⇒@K⊥<⇒@K⊥2!<3 2_3 ?D N!@%!K⇒N%@K⇒N%⊥2!<3 2__3 )2_32__3#$N%" 2 OK ?D a a OK d I SCD IH OK OM SO a 2 2 2 2 1 1 1 4 3 3 ( ,( )) 2 4 3 = + = ⇒ = ⇒ = = ?D (3 SMC SNC c c c MQ SC NQ SC( . . ) ∆ = ∆ ⇒ ⊥ ⇒ ⊥ ?D · SCD SCB SC SCD SCB MQN( ) ( ) (( ),( ))∩ = ⇒ = ?D 2 2 2 2 2 2 3 4SM OM SO a a a = + = + =  SMC∆ Q 2 2 2 2 2 2 2 2 1 1 1 1 1 5 4 5 4 4 a MQ MQ MS MC a a a = + = + = ⇒ = ?D · MQ NQ MN MQN MQ NQ 2 2 2 cos . + − ⇒ = " · 0 1 120 2 MQN− ⇒ = ?D 3 ⊥<⊥!@⊂2!<32I8!@⊥2<33⇒⊥2!<3+ 8∆!@<-F@`⊥!<-4a @`⊥ ?D? a d AC BD OP OP SO OD a a a 2 2 2 2 2 2 1 1 1 1 1 5 30 ( , ) 5 3 2 6 = + = + = ⇒ = = ?D? G"  f x x x 5 ( ) 3 1 = − − 6V6b ?D f f f f( 1) 1, (0) 1 ( 1). (0) 0− = = − ⇒ − < ?D? ⇒0-&4-Ic-8 ,-YS-Z-S2]G?3 ?D N" 3 y xcot2 = ⇒ y x 2 2 sin 2 ′ = − ?D y y x x 2 2 2 2 2 2 2cot 2 2 sin 2 ′ + + = − + + ?D x x 2 2 2(1 cot 2 ) 2cot 2 2= − + + + ?D 2 2 2 2cot 2 2cot 2 2 0x x= − − + + = ?D (3 x y x 3 1 1 + = − ⇒ y x 2 4 ( 1) ′ = − ?D? k y (2) 4 ′ = = ?D ⇒`Q y x4 15 = − ?D G6  f x x x 17 11 ( ) 1= − − ⇒ f x( ) 6V6b ?D f2?3"] f 17 11 11 6 (2) 2 2 1 2 (2 1) 1 0= − − = − − > ⇒ f f(0). (2) 0< ?D? ⇒0-&4-c-8 ,-YS-Z ?D N6 3 x y x 3 4 − = + ⇒ y y x x 2 3 7 14 ' " ( 4) ( 4) − = ⇒ = + + ?D y x x 2 4 4 49 98 2 2. ( 4) ( 4) ′ = = + + 2_3 ?D x y y x x x x x 3 3 4 3 14 7 14 98 ( 1) 1 . . 4 4 ( 4) ( 4) ( 4)   − − − − ′′ − = − = =  ÷ + + + + +   2__3 ?D d2_32__3#$Q y y y 2 2 ( 1) ′ ′′ = − ?D (3 9450$5E UIQ x y2 2 5 0 + − = 650$5 -Z#W k" ?D  x y 0 0 ( ; ) 8FS50+  x f x k x x x 0 2 0 0 2 0 0 1 4 ( ) 1 ( 1) 4 ( 1) 3  = − ′ = ⇔ = ⇔ − = ⇔  − =   ?D 9U x y PTTT y x 0 0 1 1 : = − ⇒ = − ⇒ = ?D 9U x y PTTT y x 0 0 3 5 : 8= ⇒ = − ⇒ = − ?D RS= 1*T( 2.5 điểm ):,-BU-F#Q 3  7  7 7 ++ +− nn nn (3 C L     − −+ → x xx x 3   ? > 78# +8#7  x x x x x → + − 1*=( 3 điểm ):-8-#W 7  2 3  T Dy f x x x x= = − + + − 3,- e2 3f x R(Y0-&4- ?32 e <xf 3950-&4-50$5[-\-#WF2G73+ 73-X-0-&4-f(x) = 0 ,-Y--Z0-*(Z+ 1*W( 3 điểm ): -8XIZ< <BHF-a, E U/0-12<3+N f<++-X-Q< ⊥ 2f3++-X-Q23 ⊥ 2<N3+ 7+,- .A-1f/0-12<3(5" 7  a + 1*X( 1.5 điểm ): -8-#W #  8# 8# g#  ?y x c x x x x= − + + − + +,- ey +R0-&4-Q e ?y = + Câu 1 Nội dung Điể m (2,0 điểm ) +  7  7 7 ++ +− nn nn 7 7   7     n n n n − + = + +  7 = ?+D ?+D + C L     − −+ → x xx x  2 32 73  2 32 3 x x x x x → − + = − +   7   x x x → + = + D C = ?+D ?+D 7+   ? > 78# +8#7  x x x x x → + − =   ? > 7 7 78# +8#7  x x x x x → + − + −    ? ? > 7 72 8# +8#7 3   x x x x x x x → → + − − = + ?+D    ? ?  7 2 8#  8# C 3    > 7 x x x x x x → → − + − = + + +    ?  7 2# #  3  L  x x x x → + = + ? ?  7 # +# 7 ++#  +#    L  +   + x x x x x x x x x x → → = + +  > 7  L L = + + = ?+D  Câu 2 Nội dung Điể m (3,0 điểm ) +  e2 3 7 C Tf x x x= − + +  e2 3 ? 7 C T ?f x x x< ⇔ − + + <  T 7  x x  >  ⇔  < −  ?+D ?+D +  e23 gf = `-&4-50$5F2G73$"g2hi3j7  ⇔ $"ghiD ?+D ?+D ?+D 7+  f (1)= 3 f (0)= -5 f (4)= -9       ⇒ f (1).f (0)= -15 <0 f (1).f (4)= -27 < 0    23 f   -    -X  6  6  V  6  b I8    6  V  6  k?G l   kG  Cl 23 )2323#$0-&4-f(x) = 0 ,-Y--Z0-*(Z+ ?+D ?+D ?+D Câu 3  Nội dung Điể m (3,0 điểm )  ?+D  +  ⊥ CD BJ 24BCDBH323  ⊥CD AB 4 2 3 2 3 ⊥   ⊂  AB BCD CD BCD 23 )2323#$CD ⊥ (ABJ)+ ?+D  ?+D  ?+D  ++  ⊥DI BC 24BCDBH323  ⊥ DI AB 4 2 3 2 3 ⊥   ⊂  AB BCD DI BCD 23 )2323#$DI ⊥ (ABC)  <N 2<N3 ⊂ 6(ABC) ⊥ (ADI). ?+D  ?+D  ?+D  ?+D  + f-4--5E f602<3 62f2<33"2ff3" ∧ AJB ∆AJB EF#$ 7   7 7  ∧ = = = a AB AJB BJ a !$ ? L? ∧ = AJB 9:$ .A-1f/0-12<3L? ? + ?+D  ?+D  ?+D  ?+D Câu 4 Nội dung Điể m (2,0 điểm ) + $e C8# h # h # h g8# h = + − + − ?+TD +$m"? C8# h # h # h g8# h  ?⇔ + − + − =   # h8#h # h C8# h C8# h  ? ⇔ − + + − = 23 ?+D  # h28#h 3 28#h 328# h 73 ?⇔ − + − + = 28#h 328#hj# h 73 ?⇔ − + = ?+D  <80-&4- 8#hj# h 7 ? + = E-Z6 23  8# h" h M M  7 π ⇔ ⇔ = ± + π ∈ ¢ ?+D  RSW 1*T(2,0 điểm),-BU-F#Q3  7+D  D 7 n n n n + + 3 7   2 7  3 x x x x →−∞ − + + −  1*=(2,0 điểm)4 m -#W    7 2 3 >  7 x x khi x f x x x m khi x  + − ≠  = −   + =  6VF ? 7x =  1*W(1,5 điểm),-F8-B-#W#Q3 7  7 x y x − + = − 3 C # 7y x= 1*X950-&4-50$5[-\-#W 7   C 7y x x= + − F -8-S(;  − 1*G(3,5 điểm)-8-4-- 0!+< B$-4-EF- a F-!(; a E U/ 0-12<3+3-X-Q< ⊥ 2!<3+ 3%-4--5E 6!<-X-;%E U%+ 73,- .A-1/0-12!<3+ RSX 1*T(2,0 điểm),-BU-F#Q 3 C +T  T 7 n n n n + + 3 C   2  7  3 x x x x →+∞ − + − +   1*=(2,0 điểm)4 m -#W   7 ?  2 3 C 7  x x khi x f x x m x khi x  + − ≠  = −   + =  6VF ? x =  1*W(1,5 điểm),-F8-B-#W#Q3  7  x y x − + = − 3 7 8# y c x= 1*X(1,0 điểm)950-&4-50$5[-\-#W 7   y x x= + −  F -8-S(; − 1*G(3,5 điểm)-8-4-- 0!+< B$-4-EF- a F-!(; a E U /0-12<3+ 3-X-Q< ⊥ 2!3+ 3K-4--5E 6!-X-;KE UK<+ 73,- .A-1</0-12!<3+ e RO R%F& RO [...]... 0 .25 0 .25 0.5 0 .25 0 .25 0.5 Khi x = 2 thì f (2) = 1 và x 2 − 3x + 2 ( x − 2) ( x − 1) lim f ( x) = lim = lim x 2 x 2 x 2 x 2 x 2 = lim( x − 1) = 1 x 2 ⇒ lim f ( x ) = f (2) = 1 x 2 ⇒ Hàm số liên tục tại x = 2 3 1.a Từ (1) và (2) suy ra hàm số f(x) liên tục trên ¡ Tính đạo hàm của các hàm số sau: 2 x2 + 2 x − 4 − 4 x2 − 4x − 1 y' = ( x 2 + x − 2) 2 2x2 + 2x + 5 =− 2 ( x + x − 2) 2 1.b x x y ' = 2sin... 4 x − 20 11÷ x2 − x + 2 3  = x ⇒ y '(1) = 1 − 1 + 2 = 2 , (1 + cos x) sin x − (1 + cos x)(sin x)' y' = sin 2 x 4(1đ) − sin 2 x − (1 + cos x)cos x 1 + cos x =− sin 2 x sin 2 x = x 2cos 2 1 2 − =− x x x 4sin 2 cos 2 2sin 2 2 2 2 = 0 ,25 0 ,25 0 ,25 ,  2 x   x x sin ÷ sin cos  ÷ 1  2 1 1  2 2 y" =  − = ÷= x 2  2sin 2 x ÷ 2 sin 4 x sin 4  ÷  2 2 2 , 0,5 0,5 0 ,25 sin x = 5(3đ) 4sin 4 x 2 (đ p... (sin ) ' 2 2 x x = sin cos 2 2 1 = sinx 2 (2) 0.5 0 .25 0 .25 0 .25 0 .25 0 .25 1.c 2 2.a 2. b 1   ( x 2 − x + 1) + x  2 x − ÷ 2 x 2 x  5 1 = x x+ −1 2 2 x Cho hàm số y = f(x) = x3 – 2x2 (C) 2 Ta có : y ' = 3x − 4 x y'= 1 0 .25 0 .25 0 .25 Viết phương trình tiếp tuyến của (C) tại điểm M có hồnh độ x0 = 2 Gọi M (2 ;y0) là tọa độ tiếp điểm của phương trình tiếp tuyến đồ thị hàm  f ' (2) = 4  y = f (2) = 0... 0 .25 0 .25 1) 2( x − 2) − (3 x − 2) = ( x − 2) 2 1 = ( x − 2) 2 y' = 2) y ' = 3cos 2 2 x(cos2x) ' = = −6cos 2 2 x sin 2 x = 12sin 3 3 x cos 3 x Câu 4 (1,0 điểm) 2 Tính: y ' = 6 x + 8 x y '(−1) = 2 y0 = −1 Câu 5 (3,5 điểm) 0 .25 0 .25 0 .25 0 .25 Viết đúng phương trình tiếp 0.5 tuyến 0 .25 0.5 Hình vẽ 0 .25 ⊥ AD 1) Lý luận: CD 0 .25 CD ⊥ SA 0 .25 Suy ra: CD ⊥ (SAD) 0 .25 2 Tính: y ' = 3 x + 4 x y '( 2) ... số gián đoạn tại x = 1 3 1.a (3) Từ (1), (2) và (3) suy ra hàm số f(x) liên tục trên (−∞; 1), (1; + ∞) và gián đoạn tại x = 1 Tính đạo hàm của các hàm số sau: 2 x 2 + 8x + 5 = ( x + 2) 2 0 .25 0 .25 y ' = (sinx) ' cos 3 x + s inx(cos 3 x) ' = cos 4 x - 3sin 2 x.cos 2 x 1.c 2 2.a 2. b 0 .25 0 .25 4 x 2 + 8x − 2 x 2 + 5 y'= ( x + 2) 2 1.b 0.5 ( ) y ' = 3 (2 x 2 + 3 x − 1) 2 2 x 2 + 3 x − 1 3   = 3 (2 x 2 +... 0.5 1 a 2 AC = 2 2 2 2 , SC = SA + AC = 2a OH OC OC.SA a = ⇒ OH = = SA SC SC 2 a d ( BD, SC ) = 2 Vậy, OC = 0.5 ĐỀ SỐ 7 Câu 1 Đáp án a Tính các giới hạn sau: lim x 2 x 2 − 3x + 2 x3 − 2x − 4 x 2 ( x − 2) ( x 2 x 2 = lim x →3− 2 1 10 0.5 ( x − 2) ( x − 1) = lim = lim b Điểm 2 x −1 + 2 x + 2) 0 .25 x + 2x + 2 0 .25 x +3 x −3  lim ( x + 3) = 6 > 0  x→3−   lim ( x − 3) = 0, x − 3 < 0, ∀x < 3 − Ta có: ... ⇔ y = 3x – 1 y= = 1 1 1 1 1 1 + + + cosx = 2 2 2 2 2 2 1 1 1 1 x + + cos = 2 2 2 2 2 cos2 3(1đ) = 1 1 1 1 x + + cos2 2 2 2 2 2 1 1 x 1 1 x + cos2 = + cos 2 2 4 2 2 4 x x = cos 8 8 ' 0 ,25 0,5 '  x x x 1 x y ' =  cos ÷ = −  ÷ sin = − sin 8 8 8 8  8 0 ,25 '  1 x 1 x y " =  − sin ÷ = − cos 8 64 8  8 y "(4π ) = − 1 4π 1 π cos =− cos = 0 64 8 64 2 0 ,25 ... ) 2 Kẻ AH ⊥ SB và AK ⊥ SD Chứng minh rằng : ( ( ABCD ) và ĐÁP ÁN VÀ BIỂU ĐIỂM CHẤM – TOÁN 11 - NC 3 Xác đònh và tính góc giữa hai mặt phẳng ( SBD ) Câu 1 1 Đ Nội dung f '(x) = 2 sin x + 2 cos 2x f '(x) = 0 ⇔ 2 sin 2 x + sin x − 1 = 0 1 ⇔ sin x = −1 ∨ sin x = 2 π π 5π ⇔ x = − = k2π ∨ x = + k2π ∨ x = + k2π 2 6 6 2 2 Đ 1 u1 = 2, d = 3, n = 20 0,s = 6 0100 u1q(q − 1) = 50  ⇔ 2 u1q(q − 1) = 25  2 Hpt... 0.5 x 3 − 3x 2 − 9x + 2 x3 − x + 6 0 .25 5   ®iỊu kiƯn   1 x → 2 0 .25 0.5+0 20 0  u1 =   3 ⇔ q = − 1   2 3 2 Đ Điểm 0 .25 0 .25 = lim ( x + 2 ) ( x 2 − 5x + 1) x → 2 ( x + 2 ) = lim ( x 2 − 2x + 3) x 2 − 5x + 1 x → 2 x 2 − 2x + 3 = 15 11 0.5 0.5 2 0 .25 f ( 4 ) = 1 − 4a 4 lim f ( x ) = lim x →4+ x → 4+ ( x 2 3 =L = 4 2x + 1 − 3 ) 0 .25 lim f ( x ) = lim 1 − a 4 x = 1 − 4a 4 0 .25 1 1 − Hàm số... DUNG 1 lim 2 II 1 IV 1 2 3 VIa n 4 − 2n2 + 3 = lim 5+ 1− 4 n3 2 n2 + + 0 ,25 ĐIỂM 1 n4 3 1,00 n4 = 5 2 x +4 −x = lim x →0 x →0 x 2 + x + 4 = lim x x →0 ( ) −1 2+ x +4 =− 1 4 ( x − 1)( x − 2) = lim( x − 1) = 1 x 2 x 2 và f(1) = 11 lim f ( x ) ≠ f (1) ⇒ x 2 Vậy hàm số f(x) khơng liên tục tại x0 = 2 6 2 y ' = −4 x 3 − 2 − + 10 x x y’ = tan2x + x .2. tanx.(tanx)’ = tan2x + 2x.tanx.(tan2x + 1) Hình vẽ đúng . ,-YS-Z-S 2] G?3 ?D N" 3 y xcot2 = ⇒ y x 2 2 sin 2 ′ = − ?D y y x x 2 2 2 2 2 2 2cot 2 2 sin 2 ′ + + = − + + ?D x x 2 2 2( 1 cot 2 ) 2cot 2 2= − + + + ?D 2 2 2 2cot 2 2cot 2 2 0x x=. =  SMC∆ Q 2 2 2 2 2 2 2 2 1 1 1 1 1 5 4 5 4 4 a MQ MQ MS MC a a a = + = + = ⇒ = ?D · MQ NQ MN MQN MQ NQ 2 2 2 cos . + − ⇒ = " · 0 1 120 2 MQN− ⇒ = ?D 3 ⊥<⊥!@⊂ 2! <32I8!@ 2 <33⇒ 2! <3+ 8∆!@<-F@`⊥!<-4a. + ?D? 2 1 1 1 lim 2 1 1 1 1 x x x x →+∞ + = = + + + ?D? = x x x x f x x x x 2 2 2 2( 2) 2 lim ( ) lim lim 2 ( 1)( 2) 1 → → → − = = = − − − 2 3 ?D? f23" 2 3 ?D ) 2 3 2 3#$f2x36VFx"