2019-I Cálculo Diferencial.

Información

Cálculo Diferencial. No 7847. Martes y Jueves de 2:pm a 4:pm en el 51-602.

Enlace Blackboard.

Campus Universitario.

Tutorial de Sage:

Quick references.

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