Information Technology Reference
In-Depth Information
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
300
310
320
330
340
350
360
370
b
Fig. 1.7
The graph of p.b/,whereb is the number of bagels and p.b/ is the probability that the
demand on one given day is less than or equal to b
Tabl e 1. 3
The table shows
the probability p.b/ for the
demand of bagels on one
particular day to be less than
or equal to b
b
p.b/
331
0:939
332
0:945
333
0:951
334
0:955
(b) Compute the exact integral above and compute the relative error.
(c) Use the composite trapezoidal rule (1.16) with n
D
2 to estimate the integral in
(
1.24
). Compute the relative error.
(d) Repeat (c) using n
D
3.
(e) Use the results for n
D
1; 2, and 3 to estimate how large n has to be in order for
the relative error to be less than 1/1,000.
˘
Exercise 1.2.
Let
f.x/
D
sin.x/
and
g.x/
D
sin.5x/:
(a) Compute the exact values
Z
1=2
f.x/dx
(1.25)
0
and
