Graphics Programs Reference
In-Depth Information
(d)
x
2
√
x
+
4
dx
.
(e)
−∞
e
−
x
2
dx
.
4. Compute the following integrals numerically, using
quad8
or
quadl
:
(a)
0
e
sin
x
dx
.
(b)
0
√
x
3
+
1
dx
.
(c)
−∞
e
−
x
2
dx
. In this case, also approximate the error in the numerical
answer, by comparing withthe exact answer found in Problem 3.
5. Evaluate the following limits:
(a) lim
x
→
0
sin
x
.
(b) lim
x
→−
π
1
+
cos
x
x
+
π
.
(c) lim
x
→∞
x
2
e
−
x
.
(d) lim
x
→
1
−
1
x
−
1
.
(e) lim
x
→
0
+
sin
x
.
6. Compute the following sums:
(a)
k
=
1
k
2
.
(b)
k
=
0
r
k
.
(c)
k
=
0
x
k
k
!
. You may need the gamma function
(
x
)
=
0
e
−
t
t
x
−
1
dt
,
called
gamma
in MATLAB, which satisfies
(
k
+
1)
=
k
!.
(d)
k
=−∞
1
(
z
−
k
)
2
.
7. Find the Taylor polynomial of the indicated order
n
at the indicated point
c
for the following functions:
(a)
f
(
x
)
=
e
x
,
n
=
7,
c
=
0.
(b)
f
(
x
)
=
sin
x
,
n
=
5 and 6,
c
=
0.
(c)
f
(
x
)
=
sin
x
,
n
=
6,
c
=
2.
(d)
f
(
x
)
=
tan
x
,
n
=
7,
c
=
0.
(e)
f
(
x
)
=
ln
x
,
n
=
5,
c
=
1.
(f)
f
(
x
)
=
erf(
x
),
n
=
9,
c
=
0.
8. Plot the following surfaces:
(a)
z
=
sin
x
sin
y
for
−
3
π
≤
x
≤
3
π
and
−
3
π
≤
y
≤
3
π
.
(b)
z
=
(
x
2
+
y
2
) for
−
1
≤
x
≤
1 and
−
1
≤
y
≤
1.
9. Create a 17-frame movie, whose frames show filled red circles of radius
+
y
2
)cos(
x
2
1
/
2 centered at the points
4cos(
j
π/
8)
,
4sin(
j
π/
8)
,
j
=
0
,
1
,...,
16. Make
sure all the circles are drawn on the same set of axes, and that they look
like circles, not ellipses.
10. In this problem we use the
backslash
operator, or “left-matrix-divide” op-
erator introduced in the
Solving Linear Systems
section of Chapter 4.
(a) Use the backslash operator to solve the system of linear equations
in Problem 3 of Practice Set A.
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