## 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₯+π¦+π§=2

π₯β2π¦+3π§=14

π₯+3π¦β6π§=β23

Q2. Write a program in C/C++ to determine the approximate value of the definite integral (I), by using Simpsonβs (1/3)rd rule:

I=β«π₯1/3 ππ₯,1.00.2

Using step size (β) = 0.2

Q3.Write a program in C/C++ to find the value of Sin(π/6) by using Lagrangeβs 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 βcos π₯β by using the series expansion given below:

cosπ₯=1βπ₯22!+π₯44!βπ₯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 βBisection Methodβ :

Equation:

π₯3β5π₯+1=0;π₯β[1,2]

Q6. Write a program in C/C++ to approximate the value of Integral (I), by using Trapezoidal rule : I=β«ππ₯β5+π₯10.2

Using step size (β)=0.2

Q7. Write a program in C or C++ to demonstrate the operation of the following operations, for the function π(π₯)=π₯2+π₯+7βΆ

(a) Forward Difference Operator

(b) Central Difference Operator

Q8. Write a program in C or C++ to calculate the value of ππ₯ by suing its series expansion, given below :

ππ₯=1+π₯+π₯22!+π₯33!+β―

Note: Evaluate ππ₯only upto first three terms.

Also find the value of ππ₯ by using the inbuilt function and compare it with the result produced by your program.

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