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Assignment
|
PROGRAM
|
BCA(REVISED
FALL 2012)
|
|
SEMESTER
|
3
|
|
SUBJECT CODE
& NAME
|
BCA3010-COMPUTER
ORIENTED NUMERICAL METHODS
|
|
CREDIT
|
4
|
|
BK ID
|
B1643
|
|
MAX.MARKS
|
60
|
Q.1 Determine the relative
error for the function (𝑥,,)=3𝑥2𝑦2+5𝑦2𝑧2−7𝑥2𝑧2+38
Where
x = y = z = 1 and Δ𝑥=−0.05, Δ𝑦=0.001, Δ𝑧=0.02
Answer:- Relative error:- Let the
true value of a quantity be x and the measured or inferred value x_0. Then the
relative error is defined by:
where Delta x is the absolute
error. The relative error of the quotient or product of a number of quantities
is less than or equal to the sum of their relative errors. The percentage error
is 100% times the relative error.
Q.2 Solve by Gauss
elimination method.
2x + y + 4z = 12
4x + 11y – z = 33
8x – 3y + 2z = 20
Answer: - Given equation is:
-
2x + y + 4z = 12 -------------------------------------------- (1)
4x + 11y – z = 33 --------------------------------- (2)
8x – 3y + 2z = 20----------------------------------- (3)
Multiplying equation1 with
11 and subtract it from equation 2 we get : -
18x + 45z = 99 ---------------------------------------
Q.3 Apply Gauss – Seidal
iteration method to solve the equations
3x1 + 20x2
–x3 = –18
2x1 – 3x2
+ 20x3 = 25
20x1 + x2
– 2x3 = 17
Answer: - In Gauss seidal method the latest values of unknowns at each stage
of iteration are used in proceeding to the next stage of iteration.
Let the rearranged
form of a given set of equation be
Q.4 Using
the method of least squares, find the straight line y = ax + b that fits the
following data:
|
X
|
0.5
|
1.0
|
1.5
|
2.0
|
2.5
|
3.0
|
|
Y
|
15
|
17
|
19
|
14
|
10
|
7
|
Answer: - The given straight line fit be y = ax+b. The normal equations of
least squre fit are
aSxi2 + bSxi =
Sxiyi ---------------- (1)
and aSxi
+ nb = Syi --------------------- (2)
From the given data, we have
|
x
|
y
|
xy
|
X2
|
|
0.5
|
15
|
7.5
|
0.25
|
|
1.0
|
17
|
17.0
|
1.00
|
Q.5 Using Lagrange’s
interpolation formula, find the value of y corresponding to x = 10 from the
following data:
|
X
|
5
|
6
|
9
|
11
|
|
F(x)
|
380
|
2
|
196
|
508
|
Answer:- Formula for Lagrange’s
interpolation :-
Let Y = f(x) be
a function which assumes the values f(x0), f(x1) ….. f(xn) corresponding to the
values x: x1, x1 …..x¬n.
We have x0 = 5,
x1 = 6, x2 = 9, x3 = 11
Y0 = 380, y1 = 2, y2
= 196, y3 = 508
Using Lagrange’s
Q.6 Find 𝑓′ (3), 𝑓′′ (7)
and 𝑓′′′(12) from the following data.
|
X
|
2
|
4
|
5
|
6
|
8
|
10
|
|
Y
|
10
|
96
|
196
|
350
|
868
|
1746
|
Answer:-Given data is: -
|
X
|
2
|
4
|
5
|
6
|
8
|
10
|
|
Y
|
10
|
96
|
196
|
350
|
868
|
1746
|
|
F(X)
|
2
|
4
|
5
|
6
|
8
|
10
|
Dear
students get fully solved assignments
Send
your semester & Specialization name to our mail id :
“
help.mbaassignments@gmail.com ”
or
Call
us at : 08263069601
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