Q1. Write a program in C/C++ to find the solution of system of linear equations (given below), by suing Gauss- Elimination method:
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:
Using step size (ℎ) = 0.2
Q3.Write a program in C/C++ to find the value of Sin(𝜋/6) by using Lagrange’s Interpolation, the related data is given below
x : 0 𝜋 /4 𝜋 /2
y= Sin(x) : 0 0.70711 1.0
Q4. Write a program in C/C++ to calculate the value of “cos 𝑥” by using the series expansion given below:
cos𝑥=1−𝑥22!+𝑥44!−𝑥66!+⋯Note: Evaluate cos 𝑥 only upto first three terms.
Also find the value of cos 𝑥 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 “Bisection Method” :
Q6. Write a program in C/C++ to approximate the value of Integral (I), by using Trapezoidal rule : I=∫𝑑𝑥√5+𝑥10.2
Using step size (ℎ)=0.2
Q7. Write a program in C or C++ to demonstrate the operation of the following operations, for the function 𝑓(𝑥)=𝑥2+𝑥+7∶
(a) Forward Difference Operator
(b) Central Difference Operator
Q8. Write a program in C or C++ to calculate the value of 𝑒𝑥 by suing its series expansion, given below :
Note: Evaluate 𝑒𝑥only upto first three terms.
Also find the value of 𝑒𝑥 by using the inbuilt function and compare it with the result produced by your program.