C2 02.03.2023
jueves, 2 de marzo de 2023 11:43
EXERCISES 14.1
Finding a Level Surface
In Excercises 41-44, find an equation for the level surface of the function throgh the
given point.
42. , (-1,2,1)
f
(
x
,
y
,
z
) =
l n
(
+
y
+
)
x
2
z
2
Sol:
1.- Datos y objetivos
, (-1,2,1)
f
(
x
,
y
,
z
) =
l n
(
+
y
+
)
x
2
z
2
Level surface f(x,y,z)=c
2.- Esquema
3.- Expresiones y precalculos
c
=
f
(
−
1, 2, 1) =
l n
(
+ 2 +
)
=
l n
(4)
(
−
1)
2
(1)
2
4.- Aplicación de conceptos principales
f
(
x
,
y
,
z
) =
l n
(
+
y
+
)
=
c
=
l n
(
4
)
x
2
z
2
+
y
+ = 4
x
2
z
2
OMPUTER EXPLORATIONS
Explicit Surfaces
Use a CAS to perform the following steps for each of the functions in Exercises 49–52.
a. Plot the surface over the given rectangle.
b. Plotseverallevelcurvesintherectangle.
c. Plot the level curve of ƒ through the given point.
52. , , ,
f
(
x
,
y
) =
si n
(
+
)
e
(
−
y
)
x
0.1
x
2
y
2
0
≤
x
≤
2
𝜋
−
2
𝜋
≤
y
≤
𝜋
P
(
𝜋
,
−
𝜋
)
Sol:
1.- Datos y objetivos
, , ,
f
(
x
,
y
) =
si n
(
+
)
e
(
−
y
)
x
0.1
x
2
y
2
0
≤
x
≤
2
𝜋
−
2
𝜋
≤
y
≤
𝜋
P
(
𝜋
,
−
𝜋
)
A) surface
f
(
x
,
y
)
B) several level curves
C) level curve of f through the given point.
2.- Graficas y esquemas
A
B
C