Graphics Programs Reference
In-Depth Information
11.
The equation of an ellipse is
x
2
a
2
y
2
b
2
/
+
/
=
1. Write aprogram thatcomputes
the length
2
a
−
1
S
=
+
(
dy
/
dx
)
2
dx
a
of the circumference to four decimal places for given
a
and
b
. Test the program
with
a
=
2 and
b
=
1.
12.
The error function, which isofimportance in statistics, is definedas
x
2
√
π
e
−
t
2
dt
erf(
x
)
=
0
Write aprogram that uses Gauss-Legendrequadraturetoevaluate erf(
x
)fora
given
x
to six decimal places. Note thaterf(
x
)
=
1
.
000 000 (correct to 6decimal
places) when
x
>
5. Test the program by verifying thaterf(1
.
0)
=
0
.
842701.
13.
B
L
A
m
L
k
The sliding weight of mass
m
is attached to a spring of stiffness
k
thathas an
undeformed length
L
.When the mass
is re
leased fromrest at
B
, the time ittakes
to reach
A
can be shown to be
t
C
√
m
=
/
k
, where
1
√
2
1
2
−
1
/
2
1
2
1
C
=
−
−
+
z
2
−
dz
0
Compute
C
to six decimal places.
Hint:
the integrand has a singularityat
z
=
1
z
2
)
−
1
/
2
.
that behaves as(1
−
14.
x
A
P
h
B
b
y
Search WWH ::
Custom Search