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• Norhafizah Khairol Anuar

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Quiz 4 Non Linear Equation 1. Given the function of 𝑓(𝑥) = 𝑥 2 − 7. Approximate √7 by using bisection method with |𝑏 − 𝑎| = 1. Iterate until |𝑓(𝑐𝑖 )| < Ɛ = 0.005.

2. You are working for MNA Company that makes floats for ABC commodes. The floating ball has a specific gravity of 0.6 and has a radius (R) of 0.055 m. You are asked to find the depth to which the ball is submerged when floating in water. The equation that gives the depth x to which the ball is submerged under water is given by: x3 - 0.165x2 + 3.993×10-4 Use the bisection method of finding roots of equations to find the depth x to which the ball is submerged under water. Conduct three iterations to estimate the root of the above equation (Hint: 0 ≤ x ≤ 2R). (8 marks)

System of Linear Equation 1. Solve the system of linear equations below by using Gauss elimination with pivoting method. 3x3 +4x4 =8 2x1 +9x2 +x3 =6 x2 +9x3 +4x4 =8 2x1 +x2 =9 (8 marks) 2. Modify the following system of linear equations into matrix form of Ax  b . Subsequently, solve the unknown x1 , x 2 , x3 using Gauss Elimination method. Justify your answer by using calculator.  7 x2  x1  4 x3  9

2 x3  x1  2 x2  2 x1  3x2  x3  4 (12 marks) Interpolation 1. Determine the Lagrange interpolating polynomial of f(x)=ln(x) to evaluate ln(2) on the basis of the data xo =1, x1 =4, x2 =6 and x3 =7. (10 marks)