tkz-tab.sty Làm bảng biến thiên I.pdf

Gi lnh tkz-tab.sty - Lm bng bin thin (I)

Nguyn Hu inKhoa Ton - C - Tin hc

HKHTN H Ni, HQGHN

1 Gii thiu gi lnh

Gn ay mt s bn dng tkz-tab.sty v bng bin thin. Gi lnh ny nm trong b gi lnhtng qut tkz.sty ca Alain Matthes a ch

http://altermundus.comNhng c trn CTAN:http://www.ctan.org/tex-archive/macros/latex/contrib/tkz/tkz-tabMiKTeX c gi lnh ny, bn np t chng trnh qun l gi lnh ca MiKTeX hay hn.Bn Trn Anh Tun i hc thng mi c vit mt bi v vn nyhttp://mathviet.wordpress.com/Nhng bi ca Trn Anh Tun ch cn tkz-tab.sty nguyn bn l chy c, khng cn gi

lnh tkz-tab-vn.sty. Gi lnh qu ln ti chia lm 2 bi. Ni dung hon ton ly trong hng dngi lnh ca tc gi gi lnh.

2 Mt s lnh ca gi lnh

1. Mi trng lm bng bin thin

\begin{tikzpicture}

\end{tikzpicture}

2. Cc lnh nh dng mt bng c nhiu v d\tkzTabInit[]{}{} Lnh to ra hng v

ct u tin ca bng.\tkzTabLine{} i s cc ct v trong mt hng\tkzTabVar[]{} nh dng mi

tn,cho, ngang,...

\tkzTab[]{}{}{}{}

Tng hp cc lnh trn.

2.1 Lnh thit lp hng u v ct u bng

\tkzTabInit[]{}{}

{}={e1/h1,e2/h2,...,en/hn} Mi hng c cch bng du phy,v en l biu thc no cn hn l chiu cao dng.

{}={a1,a2,...,an}Mi u ct mt biu thc an. theo cc i s sau:

Ty chn Mc nh nghaespcl 2 cm B rng ctlgt 2 cm rng ct th nhtdeltacl 0.5 cm rng ct mt v ct hai nh rng ct cui

cng vi ddng k cuilw 0.4 pt Nt k bngnocadre false Khng c ng k quanh ngoi bngcolor false Mu bng c hay khngcolorC white Mu ct th nhtcolorL white Mu hng th nhtcolorT white Mu bn trong bngcolorV white Mu ca cc bin trong bnghelp false affiche les noms des points de construction

x a1 a2 a3

espcl = 2 cm espcl = 2 cmdeltacl = 0, 5 cm deltacl = 0, 5 cm

lgt = 2 cm

V d: 1. Bng vi hng v ct

7 8

\begin{tikzpicture}\tkzTabInit{$x$/1,$f(x)$/1,$g(x)$/1}{$0$,$\E$,$+\infty$}\end{tikzpicture}

: 2

x

f (x)

g(x)

0 e +

2. Ty chn lgt

7 8

\begin{tikzpicture}\tkzTabInit[lgt=3]{ $x$ / 1}{ $1$, $3$ }\end{tikzpicture}

: 2

x 1 3

3. Ty chn espcl

7 8

\begin{tikzpicture}\tkzTabInit[lgt=3,espcl=4]%{ $x$ / 1}{ $1$ , $4$}\end{tikzpicture}

: 2

x 1 4

4. Ty chn deltacl

7 8

\begin{tikzpicture}\tkzTabInit[lgt=3,deltacl=1]%{ $x$ / 1}{ $1$ , $4$ }\end{tikzpicture}

: 2

x 1 4

5. Ty chn lw

7 8

\begin{tikzpicture}\tkzTabInit[lw=2pt]{ / 1}{ , }\end{tikzpicture}

: 2

6. Ty chn nocadre

7 8

\begin{tikzpicture}\tkzTabInit[nocadre]{ / 1, /1, /1}{ , }\end{tikzpicture}

: 2

2. Ty chn mu

7 8

\begin{tikzpicture}\tkzTabInit[color,colorT = yellow!20,colorC = orange!20,colorL = green!20,colorV = lightgray!20]{ /1 , /1}{ , }\end{tikzpicture}

: 2

7 8

\begin{tikzpicture}\tkzTabInit[color,colorT = yellow!20,colorC = red!20,colorL = green!20,colorV = lightgray!20,lgt= 1,espcl= 2.5]%{$t$/1,$a$/1,$b$/1,$c$/1,$d$/1}%{$\alpha$,$\beta$,$\gamma$}%\end{tikzpicture}

: 2

t

a

b

c

d

2.2 a mt hng vo bng

\tkzTabLine{}

\tkzTabLine{ s1,...,si,...,s(2n-1)} mi ca ct l biu thc si hoc i si s hng;z ct ng xuyn qua s 0t ng ng t ond K hai ng ng\textvisiblespace Mt lnh no

h T ng k + mang du +- mang du -

Mt lnh no V d:1. Khng i s

7 8

\begin{tikzpicture}\tkzTabInit[espcl=1.5]{$x$/ 1 ,$f(x)$ /1 }%{$v_1$ , $v_2$ , $v_3$ }%\tkzTabLine{ , , , , }\end{tikzpicture}

: 2

x

f (x)

v1 v2 v3

2. i s t

7 8

\begin{tikzpicture}\tkzTabInit[espcl=1.5]{$x$/ 1 ,$f(x)$ /1 }%{$v_1$ , $v_2$ , $v_3$ }%\tkzTabLine{ t, , t , ,t }\end{tikzpicture}

: 2

x

f (x)

v1 v2 v3

3. i s z

7 8

\begin{tikzpicture}\tkzTabInit[espcl=1.5]{$x$/ 1 ,$f(x)$ /1 }%{$v_1$ , $v_2$ , $v_3$ }%\tkzTabLine{ z, , z , ,z }\end{tikzpicture}

: 2

x

f (x)

v1 v2 v3

0 0 0

4. i s d

7 8

\begin{tikzpicture}\tkzTabInit[espcl=1.5]%{$x$ / 1,$g(x)$ / 1}%{$0$,$1$,$2$}%\tkzTabLine{d,+,0,-,d}\end{tikzpicture}

: 2

x

g(x)

0 1 2

+ 0

5. i s d v + , -

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1.5,espcl=1.75]%{$x$ / 1,$f(x)$ / 1}%{$-\infty$,$0$,$+\infty$}%\tkzTabLine{,+,d,-,}\end{tikzpicture}

: 2

x

f (x)

0 +

+

6. i s h

7 8

\begin{tikzpicture}\tkzTabInit[color,espcl=1.5]{$x$ / 1,$g(x)$ / 1}{$0$,$1$,$2$,$3$}%\tkzTabLine{z, + , d , h , d , - , t}\end{tikzpicture}

: 2

x

g(x)

0 1 2 3

0 +

2.3 Mt s v d v bng kho st du hm s

1. Dng kiu t c ng chm chm ng

7 8

\begin{tikzpicture}\tikzset{t style/.style = {style = dashed}}\tkzTabInit[espcl=1.5]{$x$ / 1 ,$f(x)$ /1 }%{$v_1$ , $v_2$ , $v_3$ }%\tkzTabLine{ t, , t , ,t }\end{tikzpicture}

: 2

x

f (x)

v1 v2 v3

2. Dng kiu z c o

7 8

\tikzset{t style/.style ={style = densely dashed}}\begin{tikzpicture}\tkzTabInit[espcl=1.5]{$x$ / 1 ,$f(x)$ /1 }%{$v_1$ , $v_2$ , $v_3$ }%\tkzTabLine{ z, , z , ,z }\end{tikzpicture}

: 2

x

f (x)

v1 v2 v3

0 0 0

3. T mu mt ct

7 8

\begin{tikzpicture}\tikzset{h style/.style = {fill=red!50}}\tkzTabInit[color,espcl=1.5]%{$x$ / 1,$g(x)$ / 1}%{$0$,$1$,$2$,$3$}%\tkzTabLine{z,+,d,h,d,-,t}\end{tikzpicture}

: 2

x

g(x)

0 1 2 3

0 +

4. ng k cho

7 8

\begin{tikzpicture}\tikzset{h style/.style ={pattern=north west lines}}\tkzTabInit[color,espcl=1.5]%{$x$ / 1,$g(x)$ / 1}%{$0$,$1$,$2$,$3$}%\tkzTabLine{z,+,,h,d,-,t}\end{tikzpicture}

: 2

x

g(x)

0 1 2 3

0 +

5.Hm gi tr tuyt i

7 8

\begin{tikzpicture}\tkzTabInit[lgt=2,espcl=1.75]%{$x$/1,$2-x$/1, $\vert 2-x \vert $/1}%{$-\infty$,$2$,$+\infty$}%\tkzTabLine{ , + , z , - , }\tkzTabLine{ , 2-x ,z, x-2, }\end{tikzpicture}

: 2

x

2 x

|2 x|

2 +

+ 0

2 x 0 x 2

6. Bng xt du

7 8

\begin{tikzpicture}\tkzTabInit[lgt=3,espcl=1.5]%{$x$/1,$x^2-3x+2$/1,$(x-\E)\ln x$/1,$\dfrac{x^2-3x+2}{(x-\E)\ln x}$ /2}{$0$, $1$, $2$, $\E$,$+\infty$}\tkzTabLine{ t,+,z,-,z,+,t,+,}\tkzTabLine{ d,+,z,-,t,-,z,+,}\tkzTabLine{ d,+,d,+,z,-,d,+,}\end{tikzpicture}

: 2

x

x2 3x + 2(x e) ln x

x2 3x + 2(x e) ln x

0 1 2 e +

+ 0 0 + +

+ 0 0 +

+ + 0 +

7. Nu 0 ta vit ax2 + bx + c = a

x b b2 4ac2a

x b +b2 4ac2a

7 8

\begin{tikzpicture}\tkzTabInit[color,lgt=5,espcl=3]%{$x$ / .8,$\Delta>0$\\ Du ca\\ $ax^2+bx+c$ /1.5}%{$-\infty$,$x_1$,$x_2$,$+\infty$}%

\tkzTabLine{ , \genfrac{}{}{0pt}{0}{\text{du ca}}{a}, z, \genfrac{}{}{0pt}{0}{\text{ngc}}{\text{du ca}\ a}, z, \genfrac{}{}{0pt}{0}{\text{du ca}}{a}, }

\end{tikzpicture}

: 2

x

> 0Du ca

ax2 + bx + c

x1 x2 +du ca

a0

ngcdu ca a

0 du caa

8. Nu < 0 khi ax2 + bx + c = a"

x +b2a

2

b2 4ac4a2

#

7 8

\begin{tikzpicture}\tkzTabInit[color,lgt=5,espcl=5]%{$x$/.8,$\Delta

2.4 Lnh a dng c cc chiu mi tn

\tkzTabVar[]{}

C th l \tkzTabVar[]{el(1),...,el(n)}Trong mi el(i)=s(i)/e(i) vi s(i) l mt k hiu iu khin v e(i) l mt gi tr s

hoc biu thc.

\newcommand*{\va}{\colorbox{red!50}{$\scriptscriptstyle V_a$}}\newcommand*{\vb}{\colorbox{blue!50}{$\scriptscriptstyle V_b$}}\newcommand*{\vbo}{\colorbox{blue!50}{$\scriptscriptstyle V_{b1}$}}\newcommand*{\vbt}{\colorbox{yellow!50}{$\scriptscriptstyle V_{b2}$}}\newcommand*{\vc}{\colorbox{gray!50}{$\scriptscriptstyle V_c$}}\newcommand*{\vd}{\colorbox{magenta!50}{$\scriptscriptstyle V_d$}}\newcommand*{\ve}{\colorbox{orange!50} {$\scriptscriptstyle V_e$}}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=2,espcl=3]{$x$/1,$f(x)$/1,$f(x)$/3}{$0$,$1$,$2$,$+\infty$}%\tkzTabLine{t,-,d,-,z,+,}%\tkzTabVar{+/\va , -D+/\vb/\vc,-/\vd, +D/\ve}%\end{tikzpicture}

: 2

x

f (x)

f (x)

0 1 2 +

0 +VaVa

Vb

Vc

VdVd

Ve

1. iu khin bng {+ /\va , -/\vb }

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%{+ /\va , -/\vb }\end{tikzpicture}

: 2

a bVaVa

VbVb

2. iu khin bng {-/\va , +/\vb}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%

{-/\va , +/\vb}\end{tikzpicture}

: 2

a b

VaVa

VbVb

3. iu khin bng {+/\va , +/\vb}

7 8


{+/\va , +/\vb}\end{tikzpicture}

: 2

a bVaVa VbVb

4. iu khin bng {-/\va , -/\vb}

7 8


{-/\va , -/\vb}\end{tikzpicture}

: 2

a b

VaVa VbVb

5. iu khin bng {+/\va , -C / \vb}

7 8


{+/\va , -C / \vb}\end{tikzpicture}

: 2

a bVaVa

VbVb

6. iu khin bng {-/\va , +C / \vb }

7 8


{-/\va , +C / \vb }\end{tikzpicture}

: 2

a b

VaVa

VbVb

7. iu khin bng {+C / \va , -C / \vb}

7 8


{+C / \va , -C / \vb }\end{tikzpicture}

: 2

a bVaVa

VbVb

8. iu khin bng {-C /\va , +C /\vb}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }

\tkzTabVar%{-C /\va , +C /\vb}\end{tikzpicture}

: 2

a b

VaVa

VbVb

9. iu khin bng { D+ /\va , -/\vb}

7 8


{ D+ /\va , -/\vb}\end{tikzpicture}

: 2

a bVa

VbVb

10. iu khin bng { D- /\va , +/\vb}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar{ D- /\va , +/\vb}\end{tikzpicture}

: 2

a b

Va

VbVb

11. iu khin bng {+/\va , -D / \vb}

7 8


{+/\va , -D / \vb}\end{tikzpicture}

: 2

a bVaVa

Vb

12. iu khin bng {-/\va , +D / \vb }

7 8


{-/\va , +D / \vb }\end{tikzpicture}

: 2

a b

VaVa

Vb

13. iu khin bng {D+ / \va , -D / \vb }

7 8


{D+ / \va , -D / \vb }\end{tikzpicture}

: 2

a bVa

Vb

14. iu khin bng {D- /\va , +D /\vb}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }

\tkzTabVar%{D- /\va , +D /\vb}\end{tikzpicture}

: 2

a b

Va

Vb

15. iu khin bng {+/ \va , -/ \vb , +/ \vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+/ \va , -/ \vb ,+/ \vc}\end{tikzpicture}

: 2

a b cVaVa

VbVb

VcVc

16. iu khin bng {+/ \va ,-C/ \vb , +/ \vc/ }

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+/ \va ,-C/ \vb , +/ \vc/ }\end{tikzpicture}

: 2

a b cVaVa

VbVb

VcVc

17. iu khin bng {- /\va , R , +/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{- /\va , R, +/\vc}\end{tikzpicture}

: 2

a b c

VaVa

VcVc

18. iu khin bng {- /\va , R , +/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2}{ a , b , c }\tkzTabVar%{- /\va , R , +/\vc}\end{tikzpicture}

: 2

a b c

VaVa

VcVc

19. iu khin bng {D-/\va , +DH/\vbo/ , }

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D-/\va , +DH/\vbo/ , }\end{tikzpicture}

: 2

a b c

Va

Vb1

20. iu khin bng {D-/\va , -DH/\va/\vb , D+/}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D-/\va , -DH/\vbo , D+/}\end{tikzpicture}

: 2

a b c

Va Vb1

21. iu khin bng {D-/\va , +D-/\vbo/\vbt , +D/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D-/\va , +D-/\vbo/\vbt , +D/\vc}\end{tikzpicture}

: 2

a b c

Va

Vb1

Vb2

Vc

22. iu khin bng {D-/\va , +D-/\vbo/\vbt , +D/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D-/\va , -D-/\vbo/\vbt , +D/\vc}\end{tikzpicture}

: 2

a b c

Va Vb1 Vb2

Vc

23. iu khin bng {+/\va , -D- / \vbo/\vbt , +/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+/ \va , -D- /\vbo/\vbt,+/\vc }\end{tikzpicture}

: 2

a b cVaVa

Vb1 Vb2

VcVc

24. iu khin bng {+ /\va,-DC- /\vbo/\vbt,+ /\vc}

7 8

\begin{tikzpicture}\tikzset{low/.style = {above = 15pt}}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+ /\va ,-DC- /\vbo/\vbt ,+ /\vc}\end{tikzpicture}

: 2

a b cVaVa

Vb1

Vb2

VcVc

25. iu khin bng {D-/\va, +DC-/\vbo/\vbt, +D/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D-/\va , +DC-/\vbo/\vbt ,+D/\vc}\end{tikzpicture}

: 2

a b c

Va

Vb1

Vb2

Vc

26. iu khin bng {D+/\va , +DC-/\vbo/\vbt , +D/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D+/\va , +DC-/\vbo/\vbt ,+D/\vc}\end{tikzpicture}

: 2

a b cVa Vb1

Vb2

Vc

27. iu khin bng {D-/\va , +CD-/\vbo/\vbt , +D/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D-/\va , +CD-/\vbo/\vbt , +D/\vc}\end{tikzpicture}

: 2

a b c

Va

Vb1

Vb2

Vc

28. iu khin bng {D-/\va , +CD-/\vbo/\vbt ,+D/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D+/\va , +CD-/\vbo/\vbt , +D/\vc}\end{tikzpicture}

: 2

a b cVa Vb1

Vb2

Vc

29. iu khin bng {+/\va, -DC+ /\vbo/\vbt, - /\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+ /\va ,-DC+ /\vbo/\vbt , -/\vc}\end{tikzpicture}

: 2

a b cVaVa

Vb1

Vb2

VcVc

30. iu khin bng {D- /\va, -DC- /\vbo/\vbt,+D/\vc}

7 8

\begin{tikzpicture}\tikzset{low/.style = {above = 15pt}}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{D- /\va , -DC- /\vbo/\vbt , +D/\vc}\end{tikzpicture}

: 2

a b c

Va Vb1

Vb2

Vc

31. iu khin bng {+/\va , -CH /\vbo/\vbt , D+/}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{+/\va , -CH /\vbo/\vbt , D+/}\end{tikzpicture}

: 2

a b cVaVa

Vb1

32. iu khin bng {+ /\va , -CH/\vb, //}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar%{+ /\va , -CH/\vb, //}\end{tikzpicture}

: 2

a b cVaVa

Vb

33. iu khin bng {+/\va , -V- /\vbo /\vbt, +/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+/\va,-V- /\vbo /\vbt, +/\vc}\end{tikzpicture}

: 2

a b cVaVa

Vb1 Vb2

VcVc

34. iu khin bng {+/ \va ,-V+ / \vbo/ \vbt ,-/ \vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+/ \va ,-V+ / \vbo/ \vbt ,-/ \vc}\end{tikzpicture}

: 2

a b cVaVa

Vb1

Vb2

VcVc

35. iu khin bng {+/ \va ,+V- /\vbo/ \vbt , -/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{+/ \va ,+V- / \vbo/ \vbt , -/\vc}\end{tikzpicture}

: 2

a b cVaVa Vb1

Vb2 VcVc

36. iu khin bng {-/ \va, +V+ / \vbo/\vbt, -/\vc}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2.5]{ /0.5,/2 }{ a , b , c }\tkzTabVar{-/ \va ,+V+ / \vbo / \vbt, -/\vc}\end{tikzpicture}

: 2

a b c

VaVa

Vb1 Vb2

VcVc

37. iu khin bng {-/ \va ,+H/\vb,-/\vc, +/ \vd}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=3]{ /0.5,/2 }{ a , b , c , d }\tkzTabVar {-/ \va ,+H/\vb,-/\vc, +/ \vd}\end{tikzpicture}

: 2

a b c d

VaVa

Vb

VcVc

VdVd

38. iu khin bng {+/ \va ,-H/\vb,-/\vc, +/ \vd}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=3]{ /0.5,/2 }{ a , b , c , d }\tkzTabVar {+/ \va ,-H/\vb,-/\vc, +/ \vd}\end{tikzpicture}

: 2

a b c dVaVa

Vb VcVc

VdVd

39. iu khin bng {-/ \va , R , R , R , +/ \ve}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=3]{ /0.5,/2 }{ a , b , c , d , e}\tkzTabVar {-/ \va ,R,R,R, +/ \ve}\end{tikzpicture}

: 2

a b c d e

VaVa

VeVe

40. iu khin bng {-/ \va , +/\vb , -DH/\vc , -/\vd , +/ \ve}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=3]{ /0.5,/2 }{ a , b , c , d , e}\tkzTabVar {-/ \va ,+/\vb ,-DH/\vc,-/\vd, +/ \ve}\end{tikzpicture}

: 2

a b c d e

VaVa

VbVb

Vc VdVd

VeVe

41. iu khin bng {D-/ \va , +DH/\vb/ , D-/\vc , +/\vd , +D/\ve}

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=3]{ /0.5,/2 }{ a , b , c , d , e}\tkzTabVar {D-/ \va ,+DH/\vb/,D-/\vc,+/\vd, -D/ \ve}\end{tikzpicture}

: 2

a b c d e

Va

Vb

Vc

VdVd

Ve

2.5 nh dng li phong cch

1. t li \tikzset{h style/.style = {fill=gray,opacity=0.4}}v mng ct t mu.

7 8

\begin{tikzpicture}\tikzset{h style/.style = {fill=red!50}}\tkzTabInit[lgt=1,espcl=2]{$x$ /1, $f$ /2}{$0$,$1$,$2$,$3$}%\tkzTabVar{+/ $1$ / , -CH/ $-2$ / , +C/ $5$, -/ $0$ / }\end{tikzpicture}

: 2

x

f

0 1 2 3

11

2

55

00

2. t gch cho khc

7 8

\verb!\tikzset{h style/.style = {pattern=north west lines}}!\begin{tikzpicture}\tikzset{h style/.style = {pattern=north west lines}}\tkzTabInit[lgt=1,espcl=2]{$x$ /1,$f$ /2}{$0$,$1$,$2$,$3$}%\tkzTabVar{+/ $1$ / , -CH/ $-2$ / , +C/ $5$, -/ $0$ / }\end{tikzpicture}

: 2

\tikzset{h style/.style = {pattern=north west lines}}

x

f

0 1 2 3

11

2

55

00

3. nh ngha li mi tn

7 8

\begin{tikzpicture}\tikzset{arrow style/.style = {blue,

->,> = latex,shorten > = 6pt,shorten < = 6pt}}

\tkzTabInit[espcl=5]{$x$ /1, $\ln x +1$ /1.5, $x \ln x$ /2}%{$0$ ,$1/\E$ , $+\infty$}%

\tkzTabLine{d,-,z,+,}\tkzTabVar%{ D+/ / $0$ ,%

-/ \colorbox{black}{\textcolor{white}{$\dfrac{-1}{e}$}}/ ,%+/ $+\infty$ / }%

\end{tikzpicture}

: 2

x

ln x + 1

x ln x

0 1/e +

0 +

01e1e

++

4. Khoanh im cui

7 8

\begin{tikzpicture}\tikzset{node style/.append style= {draw,circle,fill=red!40,opacity=.4}}\tkzTabInit[espcl=5]{$x$ /1, $\ln x +1$ /1.5, $x \ln x$ /2}%

{$0$ ,$1/\E$ , $+\infty$}%\tkzTabLine{d,-,z,+,}\tkzTabVar { D+/ / $0$ ,%-/ \colorbox{black}{\textcolor{white}{$\dfrac{-1}{e}$}}/ ,%+/ $+\infty$ / }%\end{tikzpicture}

: 2

x

ln x + 1

x ln x

0 1/e +

0 +

01e1e

++

2.6 V d kt hp

2.6.1 Hm ngc

Xt hm ngc i : x 7 1x trn ] ; 0[]0 ; +[

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1.5,espcl=6.5]{$x$ /1,$i(x)$ /1,$i$ /3}

{$-\infty$,$0$,$+\infty$}%\tkzTabLine{,-,d,-,}\tkzTabVar{+/ $0$ / ,-D+/ $-\infty$ / $+\infty$ , -/ $0$ /}

\end{tikzpicture}

: 2

x

i(x)

i

0 +

00

+

00

2.6.2 Hm tng t m v cng n dng v cng

7 8

\begin{tikzpicture}\tkzTabInit[espcl=4]{$x$ /1,$f(x)$ /1,$f(x)$ /2}

{$0$ , $1$ ,$2$, $+\infty$}%\tkzTabLine {d,+ , z,+ , z,+ , }\tkzTabVar{D-/ / $-\infty$,R/ /,R/ /,+/ $+\infty$ /}%\end{tikzpicture}

: 2

x

f (x)

f (x)

0 1 2 +

+ 0 + 0 +

++

2.6.3 Min gin on

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2]{$x$ /1, $f$ /2}{$0$,$1$,$2$,$3$}%\tkzTabVar{+/ $1$ / ,-DH/ $-\infty$ / ,D+/ / $+\infty$, -/ $2$ / }\end{tikzpicture}

: 2

x

f

0 1 2 3

11

+

22

2.6.4 Min gin on v gim lin t

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2]{$x$ /1, $f$ /2}{$0$,$1$,$2$,$3$}%\tkzTabVar{+/ $1$ / ,-CH/ $-2$ /, D+/ / $+\infty$,-/ $2$ / }\end{tikzpicture}

: 2

x

f

0 1 2 3

11

2

+

22

2.6.5 Min gin on v hai khong xc nh

7 8

\begin{tikzpicture}\tkzTabInit[lgt=1,espcl=2]{$x$ /1, $f$ /2}{$0$,$1$,$2$,$3$}%\tkzTabVar{+/ $1$ / , -CH/ $-2$ / , +C/ $5$, -/ $0$ / }\end{tikzpicture}

: 2

x

f

0 1 2 3

11

2

55

00

2.6.6 Hm c hng trn on

7 8

\begin{tikzpicture}\tkzTab[nocadre,lgt=3,espcl=4]{$x$ /1,Du \\ ca $f(x)$ /1.5,Bin thin\\ ca\\ $f$ /2}{$-\infty$, $-2$,$\dfrac{1}{\E}$,$\E$}%{z, ,d, -, d, \genfrac{}{}{0pt}{0}{\text{du ca}}{ a}, d}{+/ $\dfrac{2}{3}$, +/ $\dfrac{2}{3}$,-D-/ $-\infty$ / $-\infty$,+D/ $+\infty$ }

\end{tikzpicture}

: 2

x

Duca f (x)

Bin thincaf

2 1e

e

0 < 0 > du caa

2323

2323

+

2.6.7 Bin thin hai hm

7 8

\begin{tikzpicture}\tkzTabInit[espcl=6]

{$x$ /1, $f{x}$ /1,$f(x)$ /2, $f(x)$ /2}%{$0$ , $1$ , $+\infty$ }%

\tkzTabLine{d,+,z,-, }%\tkzTabVar {D-/ /$1$,+/ $\E$ /,-/ $0$ /}%\tkzTabVar {D-/ /$-\infty$ ,R/ $0$ /, +/ $+8$ /}\end{tikzpicture}

: 2

x

f x

f (x)

f (x)

0 1 +

+ 0

1

ee

00

+8+8

3 Lnh lm bng bin thin tng qut

\tkzTab[]{}{}{}{}

Ngha l khng phi vit lnh mi hng m l cc du ngoc nhn thi. Ngha l,

\tkzTab{ e(1) / h(1) ,... ,e(p) / h(p)}{ v(1), ... ,v(n) }{ a(1),...,a(2n-1)}{ s(1) / eg(1) / ed(1), ... ,s(n) / eg(n) / ed(n)}

3.1 V d 1

7 8

\begin{tikzpicture}\tkzTab[lgt=3,espcl=5]{ $x$ / 1,

$f(x)$ / 1,Bin thin ca \\$f$ / 2}

{ $-5$ , $0$ ,$7$}{ ,-,z,+,}{ +/$25$ , -/$0$ , +/ $49$}%

\end{tikzpicture}

: 2

x

f (x)

Bin thin caf

5 0 7

0 +2525

00

4949

3.2 V d 2

Xt hm s f : x 7 x ln x trn ]0 ; +]

7 8

\begin{tikzpicture}\tkzTab[espcl=5,lgt=3]{$x$ / 1, Du ca \\$\ln x +1$ / 1.5,%Bin thin \\$f$ / 3}%{$0$ ,$1/\E$ , $+\infty$}{d,-,z,+,}{D+/ $0$,%-/ \colorbox{black}{\textcolor{white}{$\dfrac{-1}{e}$}} ,%+/ $+\infty$ }%

\end{tikzpicture}

: 2

x

Du caln x + 1

Bin thinf

0 1/e +

0 +

0

1e1e

++

3.3 V d 3

Xt hm s f : x7 x2 1 trn ] ; 1] [1 ; +[

7 8

\begin{tikzpicture}\tkzTab{ $x$ / 1, $f(x)$ / 1, $f$ / 2}%

{ $-\infty$, $-1$ ,$1$, $+\infty$}{ ,-,d,h,d,+, }{ +/$+\infty$ , -H/$0$, -/$0$ , +/ $+\infty$ }%

\end{tikzpicture}

: 2

x

f (x)

f

1 1 +

+++

0 00

++

3.4 V d 4

Xt hm s f : t7 t2t21 trn [0 ; +[

7 8

\begin{tikzpicture}\tkzTab{ $t$ / 1, Du ca\\ $f(t)$ / 2, Bin thin ca \\$f$ / 2}%

{ $0$, $1$, $+\infty$}

{ z , - , d , - , }{ +/$0$ , -D+/$-\infty$/$+\infty$, -/ $1$ }%

\end{tikzpicture}

: 2

t

Du caf (t)

Binthin ca

f

0 1 +

0

00

+

11

Gii thiu gi lnhMt s lnh ca gi lnhLnh thit lp hng u v ct u bnga mt hng vo bngMt s v d v bng kho st du hm sLnh a dng c cc chiu mi tnnh dng li phong cchV d kt hpHm ngcHm tng t m v cng n dng v cngMin gin onMin gin on v gim lin tMin gin on v hai khong xc nhHm c hng trn onBin thin hai hm

Lnh lm bng bin thin tng qutV d 1V d 2V d 3V d 4

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