INTRODUCCION AL MAPLE

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>

> f:=(x)->1/x*sin(x);

f := proc (x) options operator, arrow; sin(x)/x end...

>

function

> f(Pi/2);

2*1/Pi

> f(a+Pi);

-sin(a)/(a+Pi)

> sin(alpha+beta);

sin(alpha+beta)

> expand(%);

sin(alpha)*cos(beta)+cos(alpha)*sin(beta)

> combine(%);

sin(alpha+beta)

> P:=x^3-x+x^2-1;

P := x^3-x+x^2-1

> whattype(P);

`+`

> ?whattype

> whattype(f(1));

function

>

>

> factor(P);

(x-1)*(x+1)^2

> expand(%);

x^3-x+x^2-1

> b:=2/3;

b := 2/3

> evalf(b);

.6666666667

> sqrt(2);

sqrt(2)

> evalf(%);

1.414213562

> exp(1);

exp(1)

> evalf(%);

2.718281828

> Pi;

Pi

> evalf(Pi);

3.141592654

> Digits:=100;

Digits := 100

> evalf(sqrt(2));

1.4142135623730950488016887242096980785696718753769...

> exp(1);

exp(1)

> evalf(%);

2.7182818284590452353602874713526624977572470936999...

> Pi;

Pi

> evalf(Pi);

3.1415926535897932384626433832795028841971693993751...

> Digits:=1000:

> evalf(Pi);

>

3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...
3.1415926535897932384626433832795028841971693993751...

> Digits:=10;

Digits := 10

>

> solve(P=0);

1, -1, -1

> solve(x^3+8);

-2, 1+I*sqrt(3), 1-I*sqrt(3)

> evalf(%);

-2., 1.+1.732050808*I, 1.-1.732050808*I

> fsolve(x^3+8);

-2.

> solve(P>=0);

-1, RealRange(1,infinity)

> plot(P,x=-2..2);

[Maple Plot]

> solve(P>-1);

RealRange(Open(-1/2-1/2*sqrt(5)),Open(0)), RealRang...

> subs(x=0,P);

-1

>

> limit(exp(k*x),x=+infinity);

limit(exp(k*x),x = infinity)

> assume(k>0);

> limit(exp(k*x),x=+infinity);

infinity

> k;

k

> k:='k';

k := 'k'

> k;

k

> solve(x^3+ln(y)=8,y);

exp(-x^3+8)

> solve({x+2*exp(y)*z+z=6,5*x+3*y=2*z,z=x^2});

{y = 1/3*RootOf(_Z+2*exp(-5/3*_Z+2/3*_Z^2)*_Z^2+_Z^...
{y = 1/3*RootOf(_Z+2*exp(-5/3*_Z+2/3*_Z^2)*_Z^2+_Z^...

> evalf(%);

{x = 1.583934298, y = -.9673252562, z = 2.508847860...

>

> solve(x^4+6*x^3-x+1=5);

RootOf(_Z^4+6*_Z^3-_Z-4,index = 1), RootOf(_Z^4+6*_...
RootOf(_Z^4+6*_Z^3-_Z-4,index = 1), RootOf(_Z^4+6*_...

> evalf(%);

.8920324889, -.4506458409+.7385325747*I, -5.9907408...

> allvalues(RootOf(_Z^4+6*_Z^3-_Z-4));

-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...
-3/2+1/12*sqrt((324*(15444+12*sqrt(1668369))^(1/3)-...

> evalf(%);

-.450645840+.7385325706*I, -.450645840-.7385325706*...

>

> g:=ln(x^2+8);

g := ln(x^2+8)

> h:=sqrt(9-(x-1)^2);

h := sqrt(8-x^2+2*x)

> plot({g,h},x=-10..10,color='red');

[Maple Plot]

> s1:=fsolve(g=h,x,-2..0);

s1 := -1.034266399

> s2:=fsolve(g=h,x,0..6);

s2 := 2.435610320

> integ_def:=int(h-g,x=s1..s2);

integ_def := 1.970962656

> integ_indef:=int(h-g,x);

integ_indef := -1/4*(-2*x+2)*sqrt(8-x^2+2*x)+9/2*ar...

> barrow:=subs(x=s2,integ_indef)-subs(x=s1,integ_indef);

barrow := 11.07331525+9/2*arcsin(.4785367734)-2.435...
barrow := 11.07331525+9/2*arcsin(.4785367734)-2.435...

> evalf(%);

1.970962663

>

> int(1/cos(x)^3,x);

1/2*sin(x)/(cos(x)^2)+1/2*ln(sec(x)+tan(x))

> int(exp(x)*sin(x),x);

-1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x)

> int(exp(-1/2*x^2),x);

1/2*sqrt(Pi)*sqrt(2)*erf(1/2*x*sqrt(2))

> int_gauss:=int(1/sqrt(2*Pi)*exp(-1/2*x^2),x=-infinity..z);

int_gauss := 1/2*erf(1/2*z*sqrt(2))+1/2

> limit(int_gauss,z=+infinity);

1

>

>

> f1:=(x)->sin(Pi*x);

f1 := proc (x) options operator, arrow; sin(Pi*x) e...

> serie_taylor_1:=taylor(f1(x),x=1,4);

serie_taylor_1 := series((-Pi)*(x-1)+1/6*Pi^3*(x-1)...

> serie_taylor_2:=taylor(f1(x),x=1,6);

serie_taylor_2 := series((-Pi)*(x-1)+1/6*Pi^3*(x-1)...

> serie_taylor_3:=taylor(f1(x),x=1,10);

serie_taylor_3 := series((-Pi)*(x-1)+1/6*Pi^3*(x-1)...

> P_taylor_1:=convert(serie_taylor_1,polynom);

P_taylor_1 := -Pi*(x-1)+1/6*Pi^3*(x-1)^3

> P_taylor_2:=convert(serie_taylor_2,polynom);

P_taylor_2 := -Pi*(x-1)+1/6*Pi^3*(x-1)^3-1/120*Pi^5...

>

> plot({f1(x),P_taylor_1,P_taylor_2},x=-1..3,y=-1..1,color=['red','blue','black'],numpoints=500);

[Maple Plot]

> ?plot

> plot([phi*sin(phi)*cos(phi),phi,phi=0..2*Pi],numpoints=1000,coords=polar);

[Maple Plot]

> plot([phi*4,phi,phi=0..10*Pi],numpoints=1000,coords=polar);

[Maple Plot]

> plot([phi^3*(1+sin(phi))^.5,phi,phi=0..6*Pi],numpoints=1000,coords=polar);

[Maple Plot]

> plot([t+5*sin(2*t), t^1.5+10*cos(2*t), t=0..10*Pi]);

[Maple Plot]

>

> plot([2+5*sin(t), 3+7*cos(t), t=0..2*Pi]);

[Maple Plot]

> g1:=(6*x^2-48*x+90)/(3*x^2-27*x+42);

g1 := (6*x^2-48*x+90)/(3*x^2-27*x+42)

> plot(g1,x=-1..10,y=-10..10);

[Maple Plot]

> limit(g1,x=infinity);

2

> g2:=(x^2-8*x+15)/(x^2-4*x+3);

g2 := (x^2-8*x+15)/(x^2-4*x+3)

> plot(g2,x=-6..10,y=-10..10);

[Maple Plot]

> limit(g2,x=1);

undefined

> subs(x=3,g2);

Error, division by zero

> limit(g2,x=3);

-1

> g3:=((x^2-8*x+15)/(x^2-4*x+3))^2;

g3 := (x^2-8*x+15)^2/((x^2-4*x+3)^2)

> plot(g3,x=-6..6,y=-1..100);

[Maple Plot]

> limit(g3,x=1);

infinity

> g1;

(6*x^2-48*x+90)/(3*x^2-27*x+42)

> plot(g1,x=-10..10,y=-10..10);

[Maple Plot]

> g1_d1:=diff(g1,x);

g1_d1 := (12*x-48)/(3*x^2-27*x+42)-(6*x^2-48*x+90)*...

> soluc:=solve(g1_d1=0);

soluc := -1-2*sqrt(6), -1+2*sqrt(6)

> g1_d2:=diff(g1,x,x);

g1_d2 := 12*1/(3*x^2-27*x+42)-2*(12*x-48)*(6*x-27)/...

> soluc[1];

-1-2*sqrt(6)

> evalf(%);

-5.898979486

> subs(x=soluc[1],g1_d2);

12*1/(3*(-1-2*sqrt(6))^2+69+54*sqrt(6))-2*(-60-24*s...
12*1/(3*(-1-2*sqrt(6))^2+69+54*sqrt(6))-2*(-60-24*s...

> simplify(%);

12*(11+4*sqrt(6))/((24+11*sqrt(6))^3)

> evalf(%);

.1887612899e-2

> imagen_soluc1:=evalf(subs(x=soluc[1],g1));

imagen_soluc1 := 1.903836718

> plot({g1,imagen_soluc1},x=-15..1,y=1.8..2,color=['black','red']);

[Maple Plot]

> soluc[2];

-1+2*sqrt(6)

> evalf(%);

3.898979486

> subs(x=soluc[2],g1_d2);

12*1/(3*(-1+2*sqrt(6))^2+69-54*sqrt(6))-2*(-60+24*s...
12*1/(3*(-1+2*sqrt(6))^2+69-54*sqrt(6))-2*(-60+24*s...

> simplify(%);

12*(-11+4*sqrt(6))/((-24+11*sqrt(6))^3)

> evalf(%);

-.5650876129

> imagen_soluc2:=evalf(subs(x=soluc[2],g1));

imagen_soluc2 := .3361632808

> plot({g1,imagen_soluc2},x=0..6,y=-1...1,color=['black','red']);

[Maple Plot]

> soluc_pto_crit_2do_ord:=solve(g1_d2);

soluc_pto_crit_2do_ord := -4*3^(1/3)-2*3^(2/3)-1, 2...

> soluc_real:=simplify(soluc_pto_crit_2do_ord[1]);

soluc_real := -4*3^(1/3)-2*3^(2/3)-1

> evalf(%);

-10.92916593

> g1_d2;

>

12*1/(3*x^2-27*x+42)-2*(12*x-48)*(6*x-27)/((3*x^2-2...

> plot(g1_d2,x=-12..-10);

[Maple Plot]

> evalf(subs(x=soluc_real,diff(g1,x,x,x)));

.7185556e-4

>

> plot(g1,x=-25..-1);

[Maple Plot]

> ?animate

>

>

> with(plots):

> animate([3*u*sin(t),2*u*cos(t),t=0..2*Pi],u=0..4,numpoints=100,frames=100);

[Maple Plot]

> animate([3*sin(t)*cos(u)+2*cos(t)*sin(u),3*sin(t)*sin(u)-2*cos(t)*cos(u),t=0..2*Pi],u=0..4*Pi,numpoints=100,frames=60,scaling=constrained,color=COLOR(RGB,1,0,1));

[Maple Plot]

>

>

>

> animate([sin(phi*u),phi,phi=-Pi..Pi],u=1..4,coords=polar,numpoints=200,frames=100,color=blue);

[Maple Plot]

> animate(sin(2*x*t),x=-3..3,t=0..1,view=-1/2..1);

[Maple Plot]

> animate( [abs(u-.5)*alpha,alpha,alpha=1..8*Pi], u=0..1,coords=polar,frames=60,numpoints=200);

[Maple Plot]

>

> animate({2*sin(5*x+0.1*t),3*sin(5*x-0.1*t)},x=0..Pi,t=0..120,frames=30,numpoints=100,color='blue');

[Maple Plot]

>

> animate([u*sin(u*phi),phi,phi=0..10*Pi],u=1..2,numpoints=500,frames=30,coords=polar,color=COLOR(RGB,1,0,1));

[Maple Plot]

>

>

>

> rand();

401594705923

> evalf(rand()/10^12);

.6294798705

> plot(sinh(x),x=-3..3,color=COLOR(RGB, rand()/10^12,rand()/10^12,rand()/10^12));

[Maple Plot]

>

> animate3d(cos(t*x)*sin(t*y),x=-Pi..Pi, y=-Pi..Pi,t=1..2,title='Gráfico_3D');

[Maple Plot]

>

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