Matemática Básica.sagews

Encontre o zeros da função $f(x)=x+x^2\sin(x)$ em um intervalo de 0 até 20.

%md **Solução**:

Solução:

f=x+x^2*sin(x)
Ox=range(0,21)
Oy=range(-200,400, 100)
plot(f,(x,0,20), figsize=[6,4],ticks=[Ox,Oy], gridlines=True)

intervalos=[(i, i+1) for i in Ox if i<20]
intervalos

[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10), (10, 11), (11, 12), (12, 13), (13, 14), (14, 15), (15, 16), (16, 17), (17, 18), (18, 19), (19, 20)]

raizes=[]
for j in intervalos:
    a=j[0]
    b=j[1]
    try:
        root = find_root(f, a, b)
    except RuntimeError:
            continue

    raizes.append(root)
print raizes

[0.0, 3.4368289123266766, 6.119024225042324, 9.529904336449029, 12.486196308339682, 15.771411695083252, 18.7963289139448]

def encontrar_todas_raizes(f,a,b):
    Ox=range(0,b+1)
    Oy=range(-200,400, 100)
    intervalos=[(i, i+1) for i in Ox if i<b]
    raizes=[]
    v=[]
    for j in intervalos:
        a=j[0]
        b=j[1]
        try:
            root = find_root(f, a, b)
        except RuntimeError:
            continue
         
        raizes.append(root)
    
    print  'Todas as raizes de', f, 'entre %d e %d:' %(a,b),'\n'
    for k in range(len(raizes)):
        print raizes[k]
        
    p=plot(f,(x,a,b), figsize=[6,4],ticks=[Ox,Oy], gridlines=True, title=f)
    return p
encontrar_todas_raizes(ln(x)*x, 1, 3)

Todas as raizes de x*log(x) entre 2 e 3: 1.0 1.0

print 'Informacao:'
    print '-----------------------------------------------------'
    print 'n','\t','Interacoes', '\t','Maior','\t','Sequencia'
    print  N, '\t', str(vezes), '\t','       ', str(maior),'    ',  sequencia
conjectura3n1()
latex(matrix([[1,1],[0,sqrt(5)/2]])

print "o velo %f" %pi

o velo 3.141593

f=x+x^2*sin(x)
a=0
b=20
Ox=range(0,b+1)
Oy=range(-200,400, 100)
plot(f,(x,a,b), figsize=[6,4],ticks=[Ox,Oy], gridlines=True, title=f)
      
raizes=[]
intervalos=[(i, i+1) for i in Ox if i<b]
for j in intervalos:
    a=j[0]
    b=j[1]
    try:
        r = find_root(f, a, b)
    except RuntimeError:
            continue

    raizes.append(r)
print  'Todas as raizes de', f, 'entre %d e %d:' %(a,b),'\n'
print raizes
p=plot(f,(x,a,b), figsize=[6,4],ticks=[Ox,Oy], gridlines=True, title=f)
save(p, 'plot_root.pdf')

Todas as raizes de x^2*sin(x) + x entre 19 e 20: [0.0, 3.4368289123266766, 6.119024225042324, 9.529904336449029, 12.486196308339682, 15.771411695083252, 18.7963289139448]

sage: f=x+x^2*sin(x)
sage: a=0
sage: b=20
sage: Ox=range(0,b+1)
sage: Oy=range(-200,400, 100)
sage: plot(f,(x,a,b), figsize=[6,4],ticks=[Ox,Oy], gridlines=True, title=f)
sage:intervalos=[(i, i+1) for i in Ox if i<b]
sage:raizes=[]
sage:for j in intervalos:
    	a=j[0]
    	b=j[1]
    	try:
        	r = find_root(f, a, b)
    	except RuntimeError:
            	continue

    	raizes.append(n(r, digits=4))
sage:print  'Todas as raizes de', f, 'entre %d e %d:' %(a,b),'\n'
sage:print raizes

Todas as raizes de x^2*sin(x) + x entre 19 e 20: [0.0000, 3.437, 6.119, 9.530, 12.49, 15.77, 18.80]

f=x + x^2*sin(x)
y0,x0=find_local_maximum(f,0,20)
y1,x1=find_local_minimum(f,0,20)

sage: plot(f,(0,20))+point((x0,y0),color='red',size=25)
 +point((x1,y1),color='red',size=25)

sage: p=plot(f,(0,20))
sage: m1=point((x0,y0),color='red',size=25)
sage: m2=point((x1,y1),color='red',size=25)
sage: p+m1+m2