Texto De Calculo II Larson Capitulo 13 Hellip

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Functions
of de
Several
Funciones
varias
Functions
of
Several
Variables
Variables
variables

13
13
13

In
this
chapter,
you
will
study
functions
of
In
Inthis
thischapter,
chapter,you
youwill
willstudy
studyfunctions
functionsof
of
En
este
capítulo
se estudiarán
funciones
more
than
one
independent
variable.
Manymore
more
than
than
one
one
independent
independent
variable.
variable.
Many
Many
In this chapter, you will study functions of
de
másconcepts
de una variable
independiente.
of
the
concepts
presented
are
extensions
of
of
ofthe
the
concepts
presented
presented
are
are
extensions
extensions
of
of
more
than
one independent
variable.
Many
Muchos
de
los
conceptos
presentados
familiar
ideas
from
earlierchapters.
familiar
familiar
ideas
ideas
from
from
earlier
earlier
chapters.
chapters.
of the concepts presented are extensions of
son extensiones de ideas familiares de
familiar
ideas from
earlier
chapters.
In
this
chapter,
you
should
learn
the
In
In
this
this chapter,
chapter,
you
you should
should learn
learn the
the
capítulos
recientes.
following.
following.
following.
In this
should learn theEn
estechapter,
capítulo,you
se aprenderá:
following.
■
How
to
sketch
graph,
level
curves,
■■
■ How
How
to
totrazar
sketch
sketchuna
aaagraph,
graph,
level
level
curves,
curves,
Cómo
gráfica,
curvas
de
and
level
surfaces.
(
13.1
)
and
level
level
surfaces.
surfaces.
(
(
13.1
13.1
)
)
■ and
nivel
y
superficies
de
nivel.
(
13.1
)
How to sketch a graph, level curves,
■
How
to
find
a
limit
anddetermine
■
■
and
level
surfaces.
13.1
) y determiHow
totoencontrar
find
find
aalimit
limit
and
determine
determine
■ How
Cómo
un(and
límite
continuity.
13.2
continuity.
(((13.2
13.2
))) and
■ continuity.
nar latocontinuidad.
(13.2
)
How
find
a limit
determine
■
How
to
find
and
use
a
partial
derivative.
■
■ How
continuity.
(
13.2
)
■
How
to
to
find
find
and
and
use
use
a
a
partial
partial
derivative.derivative.
Cómo encontrar y usar una derivada
(
13.3
)
(
(
13.3
13.3
)
)
parcial.
(13.3
) use a partial derivative.
■ How
to find
and
■
■
Cómo
y usar
unadifferential
diferenHow
to
find
and
use
total
differential
■
■ How
(How
13.3to
)toencontrar
find
findand
anduse
use
aaatotal
total
differential
cial
total
y
determinar
diferenciabili13.4
and
determine
differentiability.
and
and
determine
determinedifferentiability.
differentiability.
(((13.4
13.4)))
■ How to find and use a total differential
dad.
(
13.4
)
■
How
to
use
the
Chain
Rules
and
find
■■ How
and
13.4
Howdetermine
to
touse
usethe
thedifferentiability.
Chain
ChainRules
Rulesand
and(find
find)aaa
■ partial
Cómoderivative
usar la regla
de la cadena
derivative
implicitly.
(
13.5
)
partial
derivative
implicitly.
implicitly.
(
(
13.5
13.5)
)y a
■ partial
How to use the Chain Rules and find
encontrar
una
derivada
parcial
implí■
How
to
find
and
use
directional
■
■ How
partial
implicitly.
(13.5)
Howto
toderivative
find
findand
anduse
use
aaadirectional
directional
■
■
■
cita. (13.5
) a gradient. (13.6)
derivative
and
derivative
and
and
aagradient.
gradient.
((13.6
13.6))
■ derivative
How
to
find
and
use
a
directional
■ Cómo encontrary usar una derivada ■
■
How
to
find
an
equation
of
aatangent
tangent
■
■ How
derivative
and
aequation
gradient.
)
How
to
tofind
find
an
equation
of
of(a13.6
tangent
direccional
yanun
gradiente.
(13.6)
plane
and
an
equation
of
a
normal
line
plane
plane
and
and
an
an
equation
equation
of
of
a
a
normal
normal
line
line
■
toencontrar
find an equation
of a tangent
■ How
Cómo
unatoecuación
de
un
to
asurface,
and
how
find
the
angle
to
to
a
a
surface,
surface,
and
and
how
how
to
to
find
find
the
the
angle
angle
plane
and
an equation
of
a normal
line
plano
tangente
y
una
ecuación
de
una
of
inclination
of
plane.
((13.7
13.7
of
ofinclination
of
ofaaahow
plane.
plane.
13.7
))) angle
to
ainclination
surface,
to (find
the
recta
normaland
a una superficie,
y cómo
■
How
to
find
absolute
and
■
■ How...