Información
Cálculo Diferencial. No 7847. Martes y Jueves de 2:pm a 4:pm en el 51-602.
Desigualdades:
sage: solve(1/(x-1)<=8,x)
Definición de funciones:
sage: f(x)=x^3+1sage: f(2)
sage: show(f)
Gráficas:
sage: plot(x^2, (x,0,5))
Cálculo de límites:
sage: lim(f,x=1)
lim(f,x=1,dir='-'); lim(f,x=1,dir='right'); f(1)
Cálculo de derivadas:
sage: diff(f,x);
sage: derivative(sinh(x^2+sqrt(x-1)),x)
sage: show(derivative(sinh(x^2+sqrt(x-1)),x,3))
..
Contracciones y dilataciones de gráficas
f=sin(x)
@interact
def _(c=(4,(1,5))):
P=plot(f,x,0,2*pi,linestyle="--")
L(x)=f(x)/c
M(x)=c*f(x)
Q=plot(L,(x,0,2*pi),color="red")
R=plot(M,(x,0,2*pi),color="green")
show(P+Q+R,ymin=-5,ymax=5)
Recta tangente
f=x^3-x
@interact
def _(c=(1/3,(-2,2))):
P=plot(f,x,-2,2)
fderivada=derivative(f,x)
L(x)=fderivada(c)*(x-c)+f(c)
Q=plot(L,(x,-2,2),color="red",linestyle="--")
show(P+Q+point((c,f(c)),pointsize=40,color="red"),ymin=-2,ymax=2)
Traslaciones
f=x^2-x
@interact
def _(c=(4,(0,5))):
P=plot(f,x,-5,5,linestyle="--")
L(x)=f(x)+c
M(x)=f(x)-c
Q=plot(L,(x,-5,5),color="red")
R=plot(M,(x,-5,5),color="green")
show(P+Q+R,ymin=-5,ymax=5)
Graph transformations
P = plot(sin(x), (x,0,2*pi) )
P = P + plot(3*sin(x), (x,0,2*pi), color = 'green' )
P = P + plot(3*sin(x)+1, (x,0,2*pi), color = 'red' )
P = P + plot(3*sin(x+pi)+1, (x,-pi,pi), color = 'purple' )
P = P + plot(3*sin(2*x+pi)+1, (x,-pi,pi), color = 'black' )
P