Funcionesmaple

Grafica de funciones matematicas
Usando Maple 7
1) Graficar la funcion irracional:
> f(x):=(sqrt(x^2-1)/x);
[pic]
> solve(f(x));
[pic]
> plot(f(x),x=-10..10,y=-2..2,color=red);
[pic]
2) Graficar la funcion irracional:
> h(x):=(sqrt(x-2)/(x^2+1));
>
[pic]
> solve(h(x));
[pic]
> plot(h(x),x=-1..20,y=0..1/8,color= red);
[pic]
3) Graficar la funcion irracional:
>g(x):=((x-sqrt(x-1))/x);
[pic]
> solve(g(x));
[pic]
> plot(g(x),x=-2..30,y=0..1,color=red);
[pic]
4) Graficar la siguiente funcion:
> j(x):=((x-1)*ln(x-1)/x);
[pic]
> solve(j(x));
[pic]
> plot(j(x),x=-1..20,y=-2..3,color=red);
[pic]
5) Construir la grafica y evaluarla:
> plot(x^4-2*x^3+5*x-2,x=-4..4,y=-5..10); [pic]
[pic]
6) Grafica la funcion racional y analizala:
> plot(x/(x**2+1),x=-4..4); [pic][pic]
> solve(x/(x^2+1));
[pic]
7) Grafica la funcion irracional siguiente:
> plot(sqrt(4-x**2)+sqrt(x**2-1),x=-3..3,y=1.5..2.6);

[pic]
[pic]
8) Grafica la funcion trigonometrica:

> plot(cos(x^3)*sin(x^2),x=-3..3); [pic]
[pic]
9) Graficar la siguielte funcion:
> plot(arctan(ln(x**2-1)),x=-4..4); [pic]
[pic]
10) Grafica la funcion logaritmica:
> plot(ln(x+sqrt(1+x**2)),x=-5..5);[pic]
[pic]
11) Estudiar y representar f(x)=(x^2-5x+6)/(x^2-x-6):
> plot((x^2-5*x+6)/(x^2-x+6),x=-10..10,y=-1..2);

> plot((x^2-5*x+6)/(x^2-x+6),x=-infinity..infinity);
[pic]
12) Estudiar y graficar la siguiente funcion:
> k(x):=((2*x^3-1)/(x**2-4));
[pic]
> solve(k(x));
[pic]
> plot(k(x),x=-infinity..infinity);
[pic]
➢ plot(k(x),x=-15..15,Y=-20..20
➢
➢,discont=true);
[pic]
> limit(k(x)/x,x=infinity);
[pic]
> limit(k(x)-x,x=infinity);
[pic]
De modo que la recta y=2x es asintota oblicua
> limit(k(x)/x,x=-infinity);
>
[pic]
> limit(k(x)-x,x=-infinity);
[pic]
representar la asintota oblicua
> plot([k(x),2*x],x=-15..15,y=-20..20,discont=true,color=[red,blue]);
[pic]
13) Analizar la siguiente funcion racional:
> g(x1):=((3*x^3-1)/(2*x-1)^2);[pic]
> solve(g(x1));
[pic]
> plot(g(x1),x=-infinity..infinity);
[pic]
> plot(g(x1),x=-10..10,Y=-40..10,discont=true);
[pic]
> limit(g(x1)/x,x=-infinity);
[pic]
> limit(g(x1)/x,x=infinity);
[pic]
> limit(g(x1)-x,x=-infinity);
[pic]
> limit(g(x1)-x,x=infinity);
[pic]
> limit(g(x1)-x,x=-infinity);
[pic]
> plot([g(x1),3/4*x],x=-10..10,y=-5..5,discont=true,color=[red,blue]);
[pic]14) Analizar la funcion racional siguiente;
> g(x2):=((x**4-1)/(x+1));
[pic]
> solve(g(x2));
[pic]
> plot(g(x2),x=-infinity..infinity);
[pic]
> plot(g(x2),x=-5..5,y=-5..5,discont=true);
[pic]
> limit(g(x2)/x,x=infinity);
[pic]
> limit(g(x2)-x,x=infinity);
[pic]
no tiene asintotas
15) Graficar la funcionracional, su asintota oblicua:
> g(x3):=((x**4-5*x**2+6)/(1-x**2));
[pic]
> solve(g(x3));
[pic]
> plot(g(x3),x=-infinity..infinity);
[pic]
> plot(g(x3),x=-5..5,y=-10..10,discont=true);
[pic]
> limit(g(x3)/x,x=infinity);
[pic]
> limit(g(x3)-x,x=infinity);
[pic]
Tiene asintotas vertical x=-1,x=1;notiene asintota ablicua
16) Grafica la funcionexponencial:
> g(x4):=(x**2*exp(x)-5*x*exp(x)+6);
[pic]
> solve(g(x4));
[pic]
> plot(g(x4),x=-infinity..infinity);
[pic]
> plot(g(x4),x=-15..15,y=-230...40,discont=true);
[pic]
18) Graficar la funcion exponencial:
> g(x5):=(1-x**2)*exp((-x+1));
[pic]
> solve(g(x5));
[pic]
> plot(g(x5),x=-infinity..infinity);
[pic]
> plot(g(x5),x=-5..10,y=-10..6);
[pic]
19) Graficar la funcion racional:> g(x6):=(3/5*(x-5)*x**(2/3));
[pic]
> solve(g(x6));
[pic]
> plot(g(x6),x=-infinity..infinity);
[pic]
> plot(g(x6),x=-10..10,y=-10..10);
[pic]
20) G raficar el valor absoluto.
> g(x7):=(abs(x**3-5*x**2-x+4));
[pic]
> solve(g(x7));
[pic][pic][pic]
> plot(g(x7),x=-infinity..infinity);
[pic]
> plot(g(x7),x=-5..5,y=-2..20);
[pic]
21) Graficar y mostra su asintota oblicua:
>...