Graphics Programs Reference
In-Depth Information
Practice Set B
Calculus,Graphics,
andLinearAlgebra
Problems 2, 3, 5-7, and parts of 10-12 require the Symbolic Math Tool-
box. The others do not.
1. Use
contour
to do the following:
(a) Plot the level curves of the function
f
(
x
,
y
)
=
3
y
+
y
3
−
x
3
in the
region where
x
and
y
are between
−
1 and 1 (to get an idea of what
the curves look like near the origin), and in some larger regions (to
get the big picture).
(b) Plot the curve 3
y
+
y
3
−
x
3
=
5.
(c) Plot the level curve of the function
f
(
x
,
y
)
=
y
ln
x
+
x
ln
y
that con-
tains the point (1
,
1).
2. Find the derivatives of the following functions. If possible, simplify each
answer.
(a)
f
(
x
)
=
6
x
3
−
5
x
2
+
2
x
−
3.
2
x
−
1
x
2
(b)
f
(
x
)
=
+
1
.
(c)
f
(
x
)
=
sin(3
x
2
+
2).
(d)
f
(
x
)
=
ar
csin(2
x
+
3).
(e)
f
(
x
)
=
√
1
+
x
4
.
(f)
f
(
x
)
=
x
r
.
(g)
f
(
x
)
=
arctan(
x
2
+
1).
3. See if MATLAB can do the following integrals symbolically. For the indef-
inite integrals, check the results by differentiating.
(a)
π/
2
0
cos
xdx
.
(b)
x
sin(
x
2
)
dx
.
(c)
sin(3
x
)
√
1
−
cos(3
x
)
dx
.
86
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