Download - tkz-tab.sty Làm bảng biến thiên I.pdf
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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
\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%
{+/\va , +/\vb}\end{tikzpicture}
: 2
a bVaVa VbVb
4. 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
5. iu khin bng {+/\va , -C / \vb}
7 8
\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%
{+/\va , -C / \vb}\end{tikzpicture}
: 2
a bVaVa
VbVb
6. iu khin bng {-/\va , +C / \vb }
7 8
\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%
{-/\va , +C / \vb }\end{tikzpicture}
: 2
a b
VaVa
VbVb
7. 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 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
\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%
{ 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
\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%
{+/\va , -D / \vb}\end{tikzpicture}
: 2
a bVaVa
Vb
12. iu khin bng {-/\va , +D / \vb }
-
7 8
\begin{tikzpicture}\tkzTabInit[lgt=1]{ /0.5,/2 }{ a , b }\tkzTabVar%
{-/\va , +D / \vb }\end{tikzpicture}
: 2
a b
VaVa
Vb
13. 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 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