MAPLE PCSI 2002/2003

Episode 1 : mise en route

Exo 2

> 2+2;

> 1234^1234;

> 5/3+21/10;

> 5/3+2.1;

>

> pi;Pi;

> cos(pi);cos(Pi);

> cos(3.14);cos(3.141592654);

> if (3+3=7) then isprime(1789) else ithprime(1789) fi;

> if (3+3=6) then isprime(1789) else ithprime(1789) fi;

Exo 3

> solve({2*x+2*y-3*z=2,-2*x-y-3*z=-5,6*x+4*y+4*z=16},{x,y,z});

> solve({x+y+z+t=4,-x+y+2*z+t=2,2*x+y+3*z-t=-1,y+4*z-t=-3},{x,y,z,t});

> solve({x+y+z+t=4,-x+y+2*z+t=2,2*x+y+3*z-t=-1,y+4*z-t=4},{x,y,z,t});

pas de solution ...

Exo 4

> equa:=diff(y(t),t)+3*y(t)=2*t+3*t^2*exp(-3*t);

> dsolve(equa);

> subs(%,equa);

> simplify(%);

> evalb(%);

Exo 5

> evalf(Pi,50);

Exo 6

> sum(k^3,k=0..50);

> sum(k^3,k=0..n);

> factor(%);

Exo 7

> x=7;

> x;

> x+2;

> 7=x;

> x;

> x:=7;

> x;

> x+2;

> 7:=x;

Error, invalid left hand side of assignment

> x=9;

> evalb(x=9);

Exo 8

> x:=7;

> x+2;

> X+2;

Exo 9

> toto;

> digits;

> Digits;

> Digits:=23;

> evalf(Pi);

Exo 10

> f1:=x->2*x^2-3;

> f2:=x->exp(tan(x));

> f3:=x->x^5*sin(x)+x^4*exp(-3*x);

> f4:=x->ln(x^2+x/(cos(x)));

Exo 11

> plot(f1);

> plot(f2,-1.55..1);

Exo 12

> plot({x^2,x^4,x,sqrt(x),x^(1/3)},x=1..3,y=1..5);

> plot({x^2,x^4,x,sqrt(x),x^(1/3)},x=0..1);

Exo 13

> D(f1)(3);

Exo 14

> f:=x->x^40*exp(-1/x);

> diff(f(x),x$50);

> simplify(%);

Exo 15

> limit(ln(1+x)/(x+tan(x)),x=0);

Exo 16

> limit(f2(x),x=Pi/2);

> limit(f2(x),x=Pi/2,left);

> limit(f2(x),x=Pi/2,right);

Exo 17

> limit((1+1/n)^n,n=infinity);

> limit((1+1/n^2)^n,n=infinity);

> limit((1+1/n)^(n^2),n=infinity);

> limit((1+1/n^2)^(n^2),n=infinity);

Exo 18

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

> limit(g(x)/x,x=infinity);

> limit(g(x)-x,x=infinity);

> plot({g(x),x+3/2},x=-4..2,y=-3..3);

> asympt(g(x),x,3);

Exo 19

> int(x,x=0..1);

> int(x,x=1..2);

> int(x,x=2..3);

Exo 20

> int(sin(x)*cos(x)/(sin(x)^4+cos(x)^4),x=0..1);

>

> simplify(%);

Exo 21

> int(f3(x),x);

Exo 22

> int(exp(-x^2),x=0..infinity);