... between 0 .65 7
and 0 .66 5.
Eighth approximation: The eighth approximation to the root is given by
8
0 .65 7 0 .66 5
0 .66 1
2
x
+
==
From last two approximations, i.e.,
7
0 .6
65
x
= and
8
0 .6
61
x
= ... positive.
Therefore f (0 .67 3) is positive and f(0 .65 7) is negative so the root lies between 0 .65 7 and
0 .67 3.
ALGEBRAIC AND TRANSCENDENTAL EQUATION
41
Seventh approxi...
... the argument half way
between the arguments at q and r is
+
B
A,
24
where A is the arithmetic mean of q and r and B is arithmetic
mean of 3q – 2p – s and 3r – 2s – p.
Sol. Given A is the arithmetic ... r and s corresponds to argument a, a + h, a + 2h and a + 3h respectively
then the value of the argument lying half way between a + h and a + 2h will be
a...
... 18)
26
−− −−
×− + ×−
= 235 – 24 .65 – 10. 766 25 – 1.0 766 25
= 235 – 36. 492875
= 198.507 { 198
∴ Total no. of candidates who obtained fewer than 70 marks are 198.
Example 6. The area A of a circle of ... of candidates who obtained marks between certain limits
are as follows:
Marks
No of candidates
−−−−−0192039405 960 798099
. 41 62 65 50 17
Find no. of candidates who ob...
... dxa xdxa xdxa xdx
1111
3
5/2 2 4
012
0000
x dxa xdxa xdxa xdx=++
∫∫∫∫
or Simplifying above equations, we get
12
0
012
0
12
2
233
2
2345
2
3457
aa
a
a
aa
aaa
++=
++ =
++=
284
COMPUTER BASED NUMERICAL ... NUMERICAL AND STATISTICAL TECHNIQUES
Minimax polynomial approximation: Let f(x) be continuous on [a, b] and it is
approximated by the polynomial P
n
(x) = a
0
+ a
1
x +...
... numerical solutions of differential equations. In researches,
especially after the advent of computer, the numerical solutions of the differential equations have
become easy for manipulations. Hence, ... (Proved)
PROBLEM SET 6. 2
1. Use Trapezoidal rule to evaluate
1
3
0
xdx
∫
consisting five sub-intervals. [Ans. 0. 26]
2. Calculate an approximate value of integral
/2
0
sin...
... sensitive
to small changes in A and B i.e., small change in A or B causes a large change in the solution
of the system. On the other hand if small changes in A and B give small changes in the solution,
the ... NUMERICAL AND STATISTICAL TECHNIQUES
largest coefficient of y. We continue this process till last equation. This procedure is known as
partial pivoting. In general...
... taking suitable scale when the value of
x
are given at equally spaced intervals.
Let
h
be the width of the interval at which the values of
x
are given and let the origin of
x and y be taken ... a x b x=+
∑∑∑
(5)
The equation
()
3
and
()
4
are known as normal equations.
On solving equations
()
3
and
()
4
, we get the value of
a
and b. Putting the value of...
... the type and nature of the variations in the data.
2. The segregation and study of the various components is of paramount importance to
a businessman in the planning of future operations and in ... 1 = 64 .4
1978 2 58 + 3.4 × 2 = 64 .8
Example 8. Fit a straight-line trend equation by the method of least square and estimate the trend
value.
Year 1 961 1 962 1 963 1 964...
... 0.147=
4 76
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Sol. Mean Chart
Mean of 10 sample mean
442
44.2
10 10
x
X ===
∑
Mean Range of 10 sample ranges
58
5.8
10 10
R
R ===
∑
As we have, ... removed.
478
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
whether there are any assignable causes. If assignable causes found, the process should be
re-adjusted to...
... i);
break;
}
}
}
return 0;
}
Arrays
The declaration
int i;
declares a single variable, named i, of type int. It is also possible to declare an array of several
elements.
564
COMPUTER BASED NUMERICAL ... e
where v is any vairable (or anything like a[ i]), op is any of the binary arithmetic operators, and
e is any expression.
558
COMPUTER BASED NUMERICAL AND STATISTICA...