Tai Lieu Maple 02

8/9/2019 Tai Lieu Maple 02

1/26

Khm ph ng

1

HM S .

1) nh ngha mt hm s.C php: > f: = x > f (x) ;m s x a ta dng l > f(a); .

V d :

m s 2 3 5y f x x x .

+Nh o Maple:> f:= x -> x^2-3*x+5;

:=f x x2 3x 5

+Tnh gi tr m s1 2

3; ;

3 5

x x x .

> f(-3),f(1/3),f(-2/5);

, ,2337

9

159

25

{ n ta hi1 37 2 159

3 23; ;3 9 5 25

f f f }.

2) Xc nh hm sf t mt biu thc p(x).C php: > f: =unapply(p,x); .

V d :

Cho bi 2sin 3 2p x x x .

+ Thnh l m s o bi>p:=sin(3*x)-2*x^2;

:=p ( )sin 3x 2x2

> f:=unapply(p,x);

:=f x ( )sin 3x 2x2

+ Tnh gi tr m s18

x :

> f(Pi/18);

1

2

2

162

3) Hm s hp ca hm s f v hm s g{f(g(x))}.C php: > (f@g)(x); .

V d :

Cho hai hm s 2; 2 3y f x x y g x x .

+ Nh m s n vo Maple:


2/26

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2

> f:=x->x^2;g:=x->sqrt(2*x+3);

:=f x x2

:=g x 2x 3

m s 1h x f g x :

> h1:=(f@g)(x);:=h1 2x 3

m s 2h x g f x :

> h2:=(g@f)(x);

:=h2 2x2 3

4. Hm s nf x _{f(f(f(x)), n ch }.

C php : > (f@@n)(x);.

V d :

Cho hm s21

xf x

x.

Tm cc hm s3 4

; ;f f x f x f x .

+Nh m s

> f:=x->x/sqrt(1+x^2);

:=f xx

1 x2 +Tm cc hm s

- m s> f1:=(f@@2)(x);

:=f1x

1 x2 1x2

1 x2

Lm g> simplify(sqrt((denom(f1))^2)):f1:=numer(f1)/(%);

:=f1x

1 2x2

- m s> f2:=(f@@3)(x);


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3

:=f2x

1 x2 1x2

1 x2

1x2

( )1 x2 1 x2

1 x2

Lm g

> simplify(sqrt((denom(f2))^2)):f2:=numer(f2)/(%);

:=f2x

3x2 1

- m s(4)

(x);> f3:=(f@@4)(x):

simplify(sqrt((denom(f3))^2)):f3:=numer(f3)/(%);

:=f3x

4x2 1

Qua cc k n chng ta c th21

n xf x

nx.

5. Hm s cho bi nhiu cng thc.m s ng th dng th k

ki

V d 1:

Xt hm s2

2 1 2

2 1 2

x xy f x

x x.

(Bi t

+C th m s n trong Maple b> f:=proc(x) if x f(-1);

3

> f(-5/2);4

V d :


4/26

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4

Xt hm s2

2 2

1 1

xy f x

x x

.

Tnh2

1 ; 0,5 ; ; 1 ; 22

f f f f f .

(Bi t

+ Nh m s o Maple:> f:=proc(x)if x>=-1 and x=1 then sqrt(x^2-1)end ifend proc;

f xroc ( ):=if then elif then end ifand-1 x x 1 2 x 4 1 x ( )sqrt ^x 2 1

end proc + Tnh cc gi tr m s> f(-1);

6

> f(0.5);3.0

> a:=sqrt(2)/2:f(evalf(a));

2.585786438

> f(1);0

> f(2);

3

C th ngh m s m

piecewise theo c php sau:

>piecewise(cond1, f1, cond2, f2, );

V d :

Xt hm s2

2 2

1 1

xy f x

x x.

Tnh2

1 ; 0,5 ; ; 1 ; 22

f f f f f .

(Bi t

m s> f:=x->piecewise(x=0,x^2-x);


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:=f x ( )piecewise , , ,x 0 2x 0 x x2 x

+ Tnh cc gi tr m s

> f(sqrt(2)/2);1

2

2

2

@Nh : dng th m cho b

th m s ng th

t proc(x) ifthen.

II m s .1). V th hm sy f x .

C php: > plot( f,x,opts );> plot( f,x=x0..x1,y=y0..y1,opts );

- f: l bi

- options: cc thu

- x0.. x1: kho n tr

- y0..y1: kho n tr

* Color: Mu c cc t :

New Color Name(s) Old Color Name(s) RGB (0-255)

----------------- ---------------- ---------------

"AliceBlue" - [240, 248, 255]

"AntiqueWhite" - [250, 235, 215]

"Aqua","Cyan" "cyan" [ 0, 255, 255]

"Aquamarine" - [127, 255, 212]

- "aquamarine" [112, 219, 147]

"Azure" - [240, 255, 255]

"Beige" - [245, 245, 220]

"Bisque" - [255, 228, 196]

"Black" "black" [ 0, 0, 0]

"BlanchedAlmond" - [255, 235, 205]

"Blue" "blue" [ 0, 0, 255]

"BlueViolet" - [138, 43, 226]

"Brown" "brown" [165, 42, 42]

"Burlywood" - [222, 184, 135]

"CadetBlue" - [ 95, 158, 160]"Chartreuse" - [127, 255, 0]

"Chocolate" - [210, 105, 30]

"Coral" - [255, 127, 80]

- "coral" [255, 127, 0]

"CornflowerBlue" - [100, 149, 237]

"Cornsilk" - [255, 248, 220]

"Crimson" - [220, 20, 60]

"DarkBlue" - [ 0, 0, 139]

"DarkCyan" - [ 0, 139, 139]

"DarkGoldenrod" - [184, 134, 11]

"DarkGray","DarkGrey" - [169, 169, 169]

"DarkGreen" - [ 0, 100, 0]


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"DarkKhaki" - [189, 183, 107]

"DarkMagenta" - [139, 0, 139]

"DarkOliveGreen" - [ 85, 107, 47]

"DarkOrange" - [255, 140, 0]"DarkOrchid" - [153, 50, 204]

"DarkRed" - [139, 0, 0]

"DarkSalmon" - [233, 150, 122]

"DarkSeaGreen" - [143, 188, 143]

"DarkSlateBlue" - [ 72, 61, 139]

"DarkSlateGray","DarkSlateGrey" - [ 47, 79, 79]

"DarkTurquoise" - [ 0, 206, 209]

"DarkViolet" - [148, 0, 211]

"DeepPink" - [255, 20, 147]

"DeepSkyBlue" - [ 0, 191, 255]

"DimGray","DimGrey" - [105, 105, 105]

"DodgerBlue" - [ 30, 144, 255]

"Feldspar" - [209, 146, 117]

"Firebrick" - [178, 34, 34]

"FloralWhite" - [255, 250, 240]

"ForestGreen" - [ 34, 139, 34]

"Fuchsia","Magenta" "magenta" [255, 0, 255]

"Gainsboro" - [220, 220, 220]

"GhostWhite" - [248, 248, 255]

"Gold" - [255, 215, 0]

- "gold" [204, 127, 50]

"Goldenrod" - [218, 165, 32]

"Gray","Grey" - [128, 128, 128]

"Green" - [ 0, 128, 0]

"GreenYellow" - [173, 255, 47]

"Honeydew" - [240, 255, 240]

"HotPink" - [255, 105, 180]"IndianRed" - [205, 92, 92]

"Indigo" - [ 75, 0, 130]

"Ivory" - [255, 255, 240]

"Khaki" - [240, 230, 140]

- "khaki" [159, 159, 95]

"Lavender" - [230, 230, 250]

"LavenderBlush" - [255, 240, 245]

"LawnGreen" - [124, 252, 0]

"LemonChiffon" - [255, 250, 205]

"LightBlue" - [173, 216, 230]

"LightCoral" - [240, 128, 128]

"LightCyan" - [224, 255, 255]

"LightGoldenrod" - [238, 221, 130]

"LightGoldenrodYellow" - [250, 250, 210]

"LightGray","LightGrey" - [211, 211, 211]

"LightGreen" - [144, 238, 144]

"LightPink" - [255, 182, 193]

"LightSalmon" - [255, 160, 122]

"LightSeaGreen" - [ 32, 178, 170]

"LightSkyBlue" - [135, 206, 250]

"LightSlateBlue" - [132, 112, 255]

"LightSlateGray","LightSlateGrey" - [119, 136, 153]

"LightSteelBlue" - [176, 196, 222]

"LightYellow" - [255, 255, 224]

"Lime" "green" [ 0, 255, 0]

"LimeGreen" - [ 50, 205, 50]


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"Linen" - [250, 240, 230]

"Maroon" - [128, 0, 0]

- "maroon" [142, 35, 107]

"MediumAquamarine" - [102, 205, 170]"MediumBlue" - [ 0, 0, 205]

"MediumOrchid" - [186, 85, 211]

"MediumPurple" - [147, 112, 219]

"MediumSeaGreen" - [ 60, 179, 113]

"MediumSlateBlue" - [123, 104, 238]

"MediumSpringGreen" - [ 0, 250, 154]

"MediumTurquoise" - [ 72, 209, 204]

"MediumVioletRed" - [199, 21, 133]

"MidnightBlue" - [ 25, 25, 112]

"MintCream" - [245, 255, 250]

"MistyRose" - [255, 228, 225]

"Moccasin" - [255, 228, 181]

"NavajoWhite" - [255, 222, 173]

"Navy","NavyBlue" - [ 0, 0, 128]

- "navy" [ 35, 35, 142]

"OldLace" - [253, 245, 230]

"Olive" - [128, 128, 0]

"OliveDrab" - [107, 142, 35]

"Orange" - [255, 165, 0]

- "orange" [204, 50, 50]

"OrangeRed" - [255, 69, 0]

"Orchid" - [218, 112, 214]

"PaleGoldenrod" - [238, 232, 170]

"PaleGreen" - [152, 251, 152]

"PaleTurquoise" - [175, 238, 238]

"PaleVioletRed" - [219, 112, 147]

"PapayaWhip" - [255, 239, 213]"PeachPuff" - [255, 218, 185]

"Peru" - [205, 133, 63]

"Pink" "pink" [255, 192, 203]

"Plum" - [221, 160, 221]

- "plum" [234, 173, 234]

"PowderBlue" - [176, 224, 230]

"Purple" - [128, 0, 128]

"Red" "red" [255, 0, 0]

"RosyBrown" - [188, 143, 143]

"RoyalBlue" - [ 65, 105, 225]

"SaddleBrown" - [139, 69, 19]

"Salmon" - [250, 128, 114]

"SandyBrown" - [244, 164, 96]

"SeaGreen" - [ 46, 139, 87]

"Seashell" - [255, 245, 238]

"Sienna" - [160, 82, 45]

- "sienna" [142, 107, 35]

"Silver" "gray","grey" [192, 192, 192]

"SkyBlue" - [135, 206, 235]

"SlateBlue" - [106, 90, 205]

"SlateGray","SlateGrey" - [112, 128, 144]

"Snow" - [255, 250, 250]

"SpringGreen" - [ 0, 255, 127]

"SteelBlue" - [ 70, 130, 180]

"Tan" - [210, 180, 140]

- "tan" [219, 147, 112]


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"Teal" - [ 0, 128, 128]

"Thistle" - [216, 191, 216]

"Tomato" - [255, 99, 71]

"Turquoise" - [ 64, 224, 208]- "turquoise" [173, 234, 234]

"Violet" - [238, 130, 238]

- "violet" [ 79, 47, 79]

"VioletRed" - [208, 32, 144]

"Wheat" - [245, 222, 179]

- "wheat" [216, 216, 191]

"White" "white" [255, 255, 255]

"WhiteSmoke" - [245, 245, 245]

"Yellow" "yellow" [255, 255, 0]

"YellowGreen" - [154, 205, 50]

* style (ki : g point line patch.

* axes (d ) : g c d boxed, frame, none, normal* coords (lo bipolar, cardioid, cassinian, elliptic,hyperbolic, invcassinian, invelliptic, logarithmic, logcosh, maxwell, parabolic, polar,rose, tangent.* numpoints = n :s numpoint = 50.* thickness y c* linestyle : kiG solid, dot, dash, dashdot, longdash, spacedash, spacedot . Mc ki , ta c n

t n.

*view=[xmin..xmax, ymin..ymax] : cc kho n tr trth .

* title:* tickmarks = [a,b]: gi n

V d :

V m s siny x .

T m s sin ; sin ; siny x y x y x

(Bi t

+ V m s siny x trn kho g 2 ;2 :

>plot(sin(x),x=-2*Pi..2*Pi,title="Do thi ham so y=sin(x)tren khoang [-2Pi; 2Pi]");


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+ V m s siny x trn kho 2 ;2 :

>plot(-sin(x),x=-2*Pi..2*Pi,title="Do thi ham so y=-sin(x)tren khoang [-2Pi; 2Pi]");

+ V m s siny x trn kho 2 ;2 :

>plot(abs(sin(x)),x=-2*Pi..2*Pi,color=black,title="Do thiham so y=|sin(x)| tren khoang [-2Pi; 2Pi]");


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>plot(sin(abs(x)),x=-2*Pi..2*Pi,y=-

2..2,color=black,tickmarks=[10,10],title="Do thi ham soy=sin|x| tren khoang [-2Pi; 2Pi]");

V d :

V m s 3 3 2y x x trn kho -7; 7].

>plot(x^3-3*x+2,x=-7..7);


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Nh : Chng ta nh n tr qu l n kh

th dng

V n tr rng v tr>plot(x^3-3*x+2,x=-7..7,y=-6..6);

+N n 2 tr Maple m -10..10 cn ty . Do

>plot(x^3-3*x+2);


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@ chng ta nh rng chng ta

c ph thm cc kho y m .

* Cng c th v mt tp hp im theo tham s c ta dng [f(t), g(t)]:V d :V sin ;cosM n n v 0..20n .

> li:=[[sin(n),cos(n)] $n=0..20];li [ ],0 1 [ ],( )sin 1 ( )cos 1 [ ],( )sin 2 ( )cos 2 [ ],( )sin 3 ( )cos 3 [ ],( )sin 4 ( )cos 4, , , , ,[:=

[ ],( )sin 5 ( )cos 5 [ ],( )sin 6 ( )cos 6 [ ],( )sin 7 ( )cos 7 [ ],( )sin 8 ( )cos 8, , , ,



[ ],( )sin 17 ( )cos 17 [ ],( )sin 18 ( )cos 18 [ ],( )sin 19 ( )cos 19 [ ],( )sin 20 ( )cos 20, , , ]

+ V n:

( th nh trn, mu xanh)>plot(li,x=-2..2,y=-2..2, style=point, symbol=circle,color=blue);


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c hnh m

trong h coords=polar m s

8

1100 2 sin 7 cos30

2

1002

t t

r t

t

m s> s := t->100/(100+(t-Pi/2)^8):r := t -> s(t)*(2-sin(7*t)-cos(30*t)/2):

+ V m s>plot([r(t),t,t=-Pi/2..3/2*Pi],numpoints=2000,coords=polar,axes=normal);


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>

*V m s sin 4y x (hnh hoa tm cnh) trong h

>plot([sin(4*x),x,x=0..2*Pi],coords=polar,thickness=3,color=violet);

V nhiu th trn cng mt h trc.Ch m s n cng m .

C php:

>plot( [f,g,h], x=x1..x2, y=y1..y2, [optf, optg, opth]); .

V d :

V m s cosy x (mu xanh_ki y l 2) v

m s cosy x ( nh trn) trn cng

m>plot([cos(x), abs(cos(x))], x=-6..6,y=-2..2,

color=[blue,red],style=[line,point], symbol=circle,thickness=2, tickmarks=[10,10]);


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V th hm s cho bi nhiu cng thc:V d : (Bi t

V m s2

1 1

3 1

x xy

x x.

+ L m s> f:=proc(x) if xplot(f,-5..5,-5..6);


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2). V th ng.Gi l : > with(plots):

m s ,y f x m .

C php: > animate(plot, [f(x,m),x=a..b],m=m1..m2,option);.

Sau khi nh n mn hnh c hnh d

+Chng ta nh play (

+Mu o ta ch nt stop ( ).+

play.

+Cn trong khi kch ho play

ho play.

V d :

Kh m s 2y mx .

+ Nh o Maple:> with(plots):animate( plot, [m*x^2,x=-4..4], m=-3..3 );


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17

Trong cu l n ta cho 3; 3m n xu n mm hnh

3m .

@N h m ta nh stop

r , m

m hi n mn hnh (khung nhn ).

+ C th chm b sung

thm trong cu l n trace = n (n+1 l s m).> animate( plot, [m*x^2,x=-4..4], m=-3..3, trace=7,frames=50 );

Sau khi nh k :

b) V y f x ;M x f x chuy .

C php: >animatecurve(f(x),x=a..b, option); .

V d :

V m s cos2y x v 2 ; 2x .

> with(plots):animatecurve(cos(x),x=-2*Pi..2*Pi,frames=50);

+ Sau khi nh


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18

+K

Ghi ch: n ta c khai bo frames=50 n

trong qu trnh chuy S frames cng l ng th

d

III. M m shm sGi l : > with(Student[Calculus1]):1) Tm im cc tr ca hm s.C php: > ExtremePoints( f,x,opts );

> ExtremePoints( f,x=a..b,opts );> ExtremePoints( f,a..b,opts );

- f: l hm s x;- a..b: l kho- opts: l numeric. N true) th [a..b]=[-10..10], n

khng khai bo maple m false.

V d : Tm cc m s 4 34 2 1f x x x x .

> with(Student[Calculus1]):f:=x^3-4*x^2+2*x+1;`Cac diem cuc tri cua ham so:`;ExtremePoints( f,x );

:=f x3 4x2 2x 1

Cac diem cuc tri cua ham so:

,4

3

10

3

4

3

10

3

2) Tm im ti hn ca hm s.C php: > CriticalPoints( f,x,opts );

> CriticalPoints( f,x=a..b,opts );> CriticalPoints( f,a..b,opts );

- f: l hm s x;

- a..b: l kho


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- opts: l numeric. N true) th [a..b]=[-10..10], n


V d : Tm cc m s1

1y f x x

xtrn t

n.> with(Student[Calculus1]):f:=x+1/(x-1);`Cac diem toi han cua ham so:`;CriticalPoints( f,x );

:=f x1

x 1

Cac diem toi han cua ham so:

[ ], ,0 1 2

V d : Tm cc i m s2

1xy

x xtrn t

> with(Student[Calculus1]):f:=(x+1)/(x^2-x);`Cac diem toi han cua ham so:`;CriticalPoints( f,x );

:=fx 1

x2 x


[ ], , ,1 2 0 2 1 1

N 1;1 n:

> with(Student[Calculus1]):f:=(x+1)/(x^2-x);`Cac diem toi han cua ham so:`;CriticalPoints( f,x=-1..1 );

:=fx 1

x2 x


[ ], ,0 2 1 1

3) im un ca th hm s.C php: > InflectionPoints( f,x,opts );

> InflectionPoints( f,x=a..b,opts );> InflectionPoints( f,a..b,opts );

- f: l hm s x;

- a..b: l kho


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- opts: l numeric. N true) th [a..b]=[-10..10], n


V d : Tm honh m s

4 2

2 3y f x x x .> with(Student[Calculus1]):f:=x^4-2*x^2+3;`Hoanh do cac diem uon cua do thi ham so:`;

T:=InflectionPoints( f,x):T;

a:=eval(f,x=op(1,T)):b:=eval(f,x=op(2,T)):`Toa do cac diem uon`;{(op(1,T),a)};{(op(2,T),b)};

:=f x4 2x2 3

Hoanh do cac diem uon cua do thi ham so:

,3

3

3

3

Toa do cac diem uon

{ },3

3

22

9

{ },3

3

22

9

4) Tip tuyn ca th hm s.C php: > Tangent( f,x=c,a..b,opts );

> Tangent( f,c,a..b,opts );

- f: l hm s-

- a..b l m

N Maple s kho -1..c+1.

- opts l m : functionoptions, output,pointoptions, showfunction, showpoint, showtangent, tangentoptions, title,

view.

* functionoptions: l m u /c m s f, )c Theo m mfl m u

* output: l line slope(h plot* pointoptions: l m u /hnh d ,) cTheo m m n mu xanh(blue).

* showfunction: true ho false. N true th m s

true khi khai bo showfunction.

*showpoint: true ho false. N true th ti

v c true khi c khai bo showpoint.


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* showtangent: true ho false. N true th ti

true khi c khai bo showtangent.* tangentoptions: l m u /hnh d ,) c ti ptuy m u

xanh(blue).

*title: l chu nh v

c The Tangent to the Graph of f(x) = f(x) at the Point (c,f(c)).

*view: = [DEFAULT or a..b, DEFAULT or c..d a..b l kho

gi n tr nh; c..d l kho n tr

V d : Vi nh ti m s 3 3 1y f x x x t

01

2x .

> with(Student[Calculus1]):f:=x^3-3*x^2+1:`PT Tiep tuyen`;`y`=Tangent(f,x=1/2);

PT Tiep tuyen

y9x

4

3

2

+ N 0 0,5x , th s

> f:=x^3-3*x^2+1:`PT Tiep tuyen`; `y`=Tangent(f,x=0.5);

PT Tiep tuyen

y 2.25x 1.500

+ N

(Khai bo thm option: output = slope)

> with(Student[Calculus1]):f:=x^3-3*x^2+1:`He so goc`=Tangent(f,x=1/2,output=slope);

He so goc-9

4

+ N nh, ta th

> with(Student[Calculus1]):f:=x^3-3*x^2+1:Tangent(f,x=1/2,output=plot,pointoptions=[color=red],title="Ttuyen cua d/thi h/so f(x) tai x=1/2",view=[-1..2,DEFAULT]);


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5) ng tim cn ca th hm s.C php: > Asymptotes( f,x,y,opts );

> Asymptotes( f,x=a..b,y,opts );> Asymptotes( f,a..b,y,opts );

- f: l hm s

- a..b l kho ng khai bo_n

- y: l tn bi n, ngang,)

V d : Tm cc m s2 3 1

1

x xy f x

x.

> with(Student[Calculus1]):Tc:=Asymptotes((x^2-3*x+1)/(x - 1), x):`Tiem can xien:`=op(1,Tc);`Tiem can dung:`=op(2,Tc);

Tiem can xien: ( )y x 2

Tiem can dung: ( )x 1

V d : Tm cc ti m s 2y f x x x .

> with(Student[Calculus1]):f:=sqrt(x^2+x);`------------`;Tcan:=Asymptotes(f, x);

:=f x2 x

------------


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23

:=Tcan ,y x1

2y x

1

2

m s k : [ ] !

Ch m s 3 1y x .

> with(Student[Calculus1]):f:=x^3+1;`------------`;Tcan:=Asymptotes(f, x);

:=f x3 1

------------

:=Tcan [ ]

V d : Tm cc m s2

2

1

2 1

x xy

x xtrn kho

0;5 .

> with(Student[Calculus1]):f:=(x^2+x+1)/(2*x^2-x-1);`------------`;Tcan:=Asymptotes(f, x=0..5);

:=fx2 x 1

2x2 x 1

------------

:=Tcan ,y1

2x 1

6) ng i xngca th hm s f(x) qua ng thng y x.C php: > InversePlot( f,x,opts );

> InversePlot( f,x=a..b,opts );> InversePlot( f,a..b,opts );

- f: l hm s

- a..b l kho n tr nh c- opts : l

V d : V m s 2xy y x .

> with(Student[Calculus1]):InversePlot(2^x,x=-1..3,lineoptions=[color=black,thickness=2], title="Do thi hamnguoc cua h/so y=2^x");


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V d : V m s m s 2 1y x 1.5;1.5 .

> with(Student[Calculus1]):InversePlot(sqrt(x^2-1),x=-1.5..1.5,lineoptions=[color=black,thickness=2],title="Do thi hamnguoc cua h/so f(x)");

6) Gi tr nh nht v gi tr ln nht ca hm s.* Gi tr l nh m s :

C php: > maximize( f,x);> maximize( f,x=a..b);

* Gi tr m s :


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C php: > minimize( f,x);> minimize( f,x=a..b);

- m gi tr

l

V d

Tm gi tr gi tr m s 3 23 9 35y x x x trn

4;4 0;5 ?

(Bi t _SGK Gi , B

+ Nh m s o Maple:> y:=x^3-3*x^2-9*x+35;

:=y x3 3x2 9x 35

+ Gi tr m s 4; 4 :>minimize(y,x=-4..4);

-41

+ Gi tr m s 4; 4 :

>maximize(y,x=-4..4);40

+ Gi tr m s 0; 5 :

>minimize(y,x=0..5);8

+ Gi tr m s 0; 5 :

>maximize(y,x=0..5);40

C th m s 4;>plot(y,x=-4..5);


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* Mu m s o ta c th

sung thm t

Ch>maximize(y,x=0..5,location);,40 { }[ ],{ }x 5 40

K n cho bi max 5 40y y .

Cn trn 4;4 :

>maximize(y,x=-4..4,location);,40 { }[ ],{ }x -1 40

K4;4

max 1 40y y .

V d :

Tm gi tr m s2

11

y x xx

.

(Bi t

+ Tm trong Maple nh sau:>minimize(x+2/(x-1),x>1,location);

,2 2 1 { }[ ],{ }x 2 1 2 2 1

K 1

2min 2 2 1

1xx

x2 1x .

V d :

Tm gi tr gi tr 1 4A x x .

(Bi t o)

+ Nh 1; 4 .

>A:=sqrt(x-1)+sqrt(4-x);`gtnn`:=minimize(A,x=1..4,location);`gtln`:=maximize(A,x=1..4,location);

:=A x 1 4 x

:=gtnn ,3 { },[ ],{ }x 1 3 [ ],{ }x 4 3

:=gtln ,2 3 { },{ }x5

22 3

Qua k qu n cho ta bi

- gi tr 3 1 4x x ;- gi tr 2 3 6 5

2x .

Tai Lieu Maple 02

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