Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
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