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BCSL-058 Computer oriented Numerical techniques Lab Solved Assignment 2019-20

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Course Code : BCSL-058
Course Title : Computer oriented Numerical techniques Lab
Assignment Number (Code) : BCA(5)/L-058/Assignment/2019-20
Last Date of Submission : 15th October 2019 (for July 2019 session)
15th April 2020 (for January 2020 session)

Description

Q1. Write a program in C/C++ to find the solution of system of linear equations (given below), by suing Gauss- Elimination method:
π‘₯+𝑦+𝑧=2
π‘₯βˆ’2𝑦+3𝑧=14
π‘₯+3π‘¦βˆ’6𝑧=βˆ’23

Q2. Write a program in C/C++ to determine the approximate value of the definite integral (I), by using Simpson’s (1/3)rd rule:
I=∫π‘₯1/3 𝑑π‘₯,1.00.2
Using step size (β„Ž) = 0.2

Q3.Write a program in C/C++ to find the value of Sin(πœ‹/6) by using Lagrange’s Interpolation, the related data is given below
x : 0 πœ‹ /4 πœ‹ /2
y= Sin(x) : 0 0.70711 1.0

Q4. Write a program in C/C++ to calculate the value of β€œcos π‘₯” by using the series expansion given below:
cosπ‘₯=1βˆ’π‘₯22!+π‘₯44!βˆ’π‘₯66!+β‹―Note: Evaluate cos π‘₯ only upto first three terms.
Also find the value of cos π‘₯ by using the inbuilt function.
Compare the results i.e., the result produced by your program and that produced by inbuilt function. Based on comparison, determine error.

Q5. Write a program in C/C++ to find the root of the following equation by using β€œBisection Method” :
Equation:
π‘₯3βˆ’5π‘₯+1=0;π‘₯∈[1,2]

Q6. Write a program in C/C++ to approximate the value of Integral (I), by using Trapezoidal rule : I=βˆ«π‘‘π‘₯√5+π‘₯10.2
Using step size (β„Ž)=0.2

Q7. Write a program in C or C++ to demonstrate the operation of the following operations, for the function 𝑓(π‘₯)=π‘₯2+π‘₯+7∢
(a) Forward Difference Operator
(b) Central Difference Operator

Q8. Write a program in C or C++ to calculate the value of 𝑒π‘₯ by suing its series expansion, given below :
𝑒π‘₯=1+π‘₯+π‘₯22!+π‘₯33!+β‹―
Note: Evaluate 𝑒π‘₯only upto first three terms.
Also find the value of 𝑒π‘₯ by using the inbuilt function and compare it with the result produced by your program.

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