 !" #$%&'()*) + ,-'.($,./01%-$234) 566.)7) + 66.)8) + 8'.9.:'()*) + ,-'.($,./01%-$23#; limx→xo+f(x)=limx→xo-f(x)=f(xo) .<;=$,.$>%?%@A"     .B.;()*) C ,-'.($,./01%-$23#;,.$ )8CD *,.$ )8C *4) + E-%Flimx→0+cosxln(x) – cosxln(x + x 2 )*,.$,1/1+x +2) *C *85limx→xo-a.sinx.arccotgx= -a =0*8%*CG-fxo =0*8%*C => Kết luận:… H" IJK,./01%-$23L.'.($) C M C & limx→xolimy→yof(x,y)*limy→yolimx→xof(x,y)*lim5y→yox→xo f(x,y) NO9lim2 ≠lim (1)#P.Q'+L%M" NO9lim2 =lim (1)#)JROlim3 so với lim (1)O9,.$S *,.$! *8,./0 P9<;)J,.$?-+#?T,L.+.,-U23" )J,.$S V'WM*) ∈ R @V'WX.:)Y$Z[X O9+4) C M C *U23#)J,.$! *,.$H *4) C M C " G\]0!HStrang 7 Toán Học Cao Cấp 3" S" #$^@_-$S?`)M &; P9<,a,+.?Q,-U23@b.'L+-$ c!;=$`d)e`dM*6)J5`d)*CG-`dM*+*8Q.:$) C M C " cH;]^%G-+c!=$`dd))e`dd)Me`ddMM@b.,a,+*f*c*" cS;,XB)J'.($^@_  E. f c  g )J %MQ.:$) + M + %2hFfcG-g*c  H if O9; g8C'.($,-^@_ g*C'.($F(,-^'L.+W^R(9 g7C)JROf8C;'.($,-^R(9 f7C;'.($,-^'L.    !"#! `d)*H)MDHe`dM*) H  .B.:5`d)*CG-`dM*C*8jx=2x=-2G-jy=1/2y=-1/2*85M12;-12 M3-2;-12 M22;12 M4(-2;12) %F5z''xx=2y=Az''xy=2x=Bz''yy=2x=C XB)J'.($^@_ E. f c  g )J E! !   HC ,-'.($^@_ EH !   !H ,-'.($^@_ ES !   !H ,-'.($^@_ E !   HC ,-'.($^@_ " #$E.E%)-$`)M .A.L@+$.'FX_W[; c!;k9]l!6)J`d)G-`dM.B.:5z'y=0z'x=0*85y=yox=xo O,9m% $n[%M+ cH;*8%F`) C M C *"""! cS;k9]lH"""%F`*"""Y+!? )J`d ? *66*C*8?*? C ROXAHH c;o! H *8GM$.`*$%)`*  $  %!  &  !  &  '()*+,-   !  ≤1 -$`)Q'_G-,./0∀ x,y∈R2/'L$%)$.@+$.'F[ I;) H DM H ≤1p %F`d)*!)iH")"H) H DM H D! *)!iH) H iM H  `dM*MiH"HM"H) H DM H D! *M!i) H iHM H .B.:5z'x=0z'y=0*8j5jy=-12y=-12x=05jx=+12x=-12y=o (thỏa mãn đk(*))*8%F5z0,-12 =z0,12 =14z0,0 =0z12,0 =z-12,0 =1 ! ckM.V%)J.Q@_1%`@/X./$.'F[ với y 2 = 1 - x 2 , ∃x∈[-1,1]|∃y∈[-1,1] hệ z= x 2 – x 4 )J`d*H)) S *C*8jx=0x=±12*85z±12 =14z0 =0H P;o! H GM-$`'L$.*C$%)*!@+$.'FX_W[" " #$^@_-$!?M*4) ,-$B+2Q-$qr c!;I;""""2%9'F'L+-$XU!@+HQP+%@.NYYHGO+WL+-$" cH;=$.:$Ms cS;XBX.O./ .*/'0*y=x3x2-2x1 .B.;-$M)Q'_G-,./0@/t y'=3x2-2x+ 2x-233x2-2x=3x2-8x-33x2-2x )Jy'=0=>jx=-13x=3 -> bảng biến thiên: ZM-$M'L^'L.L.)*!uS'L^R(9L.)*S" " +q6"IQ'_-$?`)M &=$]`) C M C c!;+) + G-M C %Mq'a9=$`*& cH;G.kH,aY+H?)G-M9M(GOY+6`d)*6]) G-6`dM*6]M cS;%M:23'n=$vc!*8`d)*`dM* c;GM]`*`d)D`dM*%])DX]M%Xwxt 0*% % ! %  %  !23'0*45!6"&5&1 c!;%M)*!G-M*!G-+qp %F`*!" cH;G.kY+X.O)*8y) H ])DS` H "`d)*`])D)DM `d) *8cS;`d)*x+y-3z29x2-z])*-38]) ^*8`dM*-58]M c;GM]`!e! *`d)D`dM*-3/8 ])i5/8]M,-Oz9Ba=$" " +-$23M*4) )'5)*) =$4d) G-4dd) & M*M  *84d) *y'(t)x'(t)*84ss) *df'(x)x'(t)P9<;{'L+-$Y+X.O" !  7 "780  % %9 %F4s) *5t4-53t2+3*84ss) *532tt2+1 |" \Kk)Q'_; Qqq\;/$XA'.X.O'W?,.Q(đọc tham khảo GT I Trần Bình  ) a}Q'~O2QToán học Cao Cấp 2;  @HC|HCy$  + @H!C X H!HY 4 H!SH!X H!4 H!'}•€~<•i{]‚'.X.O H!y HHC A  *6G- ! *,+L.G-ZHHS,.Q@HHy9R/'.X.O€V]‚• HS!X  HSH] HSSi/$Q H!y"F$,,L.a.v @/J,L.Y+@\A+B3.'%SC~@b.2+2Q " y" \'ƒ] ].:K(K(Trần Bình, BT Giải Tích I, trang 351 đến 355); P9<;ai'(]„A$….a/,†M!8H,-$9?]+FK,W,L." !C" >]0G.kKa'~; c!;'WX.(9>f*4)eM GA.5x=xo+ ∆xy=yo+ ∆y cH;>]0G.k;4)M *4)+M+ D∆x.dfxx o ,y o + ∆y.dfy(x o ,y o )%M23 6: (1,04)2+(2,02)3+ 7 1 .B.;c!;'Wf*x2+y3+7*4)M GA.5x=xo+ ∆xy=yo+ ∆yGA.5xo=1; ∆x=0,04yo=2; ∆y=0,02 cH;>]0G.k4)M *4)+M+ D∆x.dfxx o ,y o + ∆y.dfy(x o ,y o ) ]4 ) * ]4 M * %M23 *8f* *DCC!DCCS*C !!" #$.A.L]‚Kk; c'}/$;@ac#c!a!CS@%SSk91→5" @#^;=$k‡X.O./9.uG.OG]Li/n[(xích ma) n/i=1]f(i) a=$]L-$4>" !H" I'.A.L,+L.!+WH; 5limx→xo+f(x)=A limx→xo-f(x)=B∀ A,B=const.Q'+L,+L.!O9A ≠ B +WA = B ≠ f(xo) Q@VQ{a ∃ !,.$* ±∞ O,9,+L.H" !S" #$R:$-$$ƒX.OG-.9X.O; -$!X.O,-$q;%G-'>X!u! )./XHu! %XuD! " -$.9X.O; 5limt→toxt =aelimt→toyt =∞=>x=a là tiệm cận đứng. 5limt→toxt =∞elimt→toyt =b=>y=b là tiệm cận ngang. 5limt→toxt =∞G-limt→toyt =∞=>và 5limt→toy(t)/x(t)=celimt→toyt - cx(t)=d =>y=cx+d là tiệm cận xiên. !" IJ2^ƒ.01%Kk29M@ƒ; c!;=$'.($) C .O$l923*C+WX.(9>+)Q'_'.($X†V" cH;;abfx =acf(x)+cbf(x)GA.) C ∈[a;c] cS;)Jƒ.0k#1%BHKk+" : 0(tích phân)+∞ sinx/[căn bậc 3của x];/<=1 %Ff*0(tích phân)1 sinx/[căn bậc 3của x] +1(tích phân)+∞ sinx/ [căn bậc 3của x]*f ! Df H F'.($X†V,-)*C )Jf ! limx→0sinx/[căn bậc 3của x] =limx→0 x/[căn bậc 3 của x]=0 *8f ! ƒ.0! )Jf H ]+limx→+∞sinx/[căn bậc 3của x] =0 hội tụ/f H *1(tích phân) +∞ sinx/[căn bậc 3của x] ƒ.0H o! G-H *8O,96 !" E%) G-X) ,-HG‚XJ{,:wt G-=$PE; NAQXBG];,.$ )8C e x -1xp *!,.$ )8C arctan xx*!limn→∞1+1n n* Ylimx→0ln (x+1)x *!6Toán Học CC tr 93)" %.@.(%M,+@trang 108, Trần Bình, BTGT 1 Pdd2.%,XmZcX%+XmZPX†6(trang 156, BTGT 1) axf(t)dt=fx - fa ∀a∈R αx =ex2 và > e-(1+x)1x?@?ABCD,CD"1 IJˆ) * e-(1+x)1x*e-e1xln (1+x)*-e( eln (1+x)x -1-1)Q]0p  *8ˆ) *-e( ln1+x x-1)%.@.(%M,+@.)8C *8ˆ) *-e( [0+x- x2+ ⍬x2 x]/2-1 )*ex2*‰) *8limx→0β(x)/α(x) =1*8O,96 !" +-$234*9) G) =$4  ) & [‚=(xích ma)k=0,nCk,n u(mũ)kv(mũ)n-kŠ‹9MŒPY.Š • P9<; N/}9,--$'%>FXm†" \†9a^1%G) .'L+-$,a" Z[;   π2.* 7% 1 .B.;%F9*) H DH*89d*H)*89dd*He9  *C∀•S G*2.)Dπ/2 *8G $ *2.)Dπ/2Dmπ/2 *C.$*HD! GM4 S ) *Ck.53 ukv53-k*C0,53 ) H DH 2.)Dπ/2+53π/2 +C1,53 H)2.)D π/2+26/π D C2,53 H2.)Dπ/2+51π/2)DC *84 S C *S"H"C"!DC*C*8O,9""" . & limx→xolimy→yof(x,y)*limy→yolimx→xof(x,y)*lim5y→yox→xo f(x,y) NO9lim2 ≠lim (1)#P.Q'+L%M" NO9lim2 =lim (1)#)JROlim3 so v i lim (1)O9,.$S. " -$.9X.O; 5limt→toxt =aelimt→toyt =∞=>x=a là tiệm cận đứng. 5limt→toxt =∞elimt→toyt =b=>y=b là tiệm cận ngang. 5limt→toxt =∞G-limt→toyt =∞=>và 5limt→toy(t)/x(t)=celimt→toyt. x]*f ! Df H F'.($X†V,-)*C )Jf ! limx→0sinx/[căn bậc 3của x] =limx→0 x/[căn bậc 3 của x]=0 *8f ! ƒ.0! )Jf H ]+limx→+∞sinx/[căn bậc 3của x] =0 h i tụ/f H *1 (tích phân) +∞ sinx/[căn bậc 3của