For a = 3.141592 and approximate value of a as 3.14 evaluate absolute error, relative error, and percentage error.
[3 marks]Find a root of x3-5x+3=0 by the bijection method correct up to four decimal places.
[4 marks]Derive the iteration formula for Nand hence , find 65.
[7 marks]Solve the following system of equations: x +3y +2z = 2x +4y 6z = x + 5y +3z =
[10 marks]Solve the following systems of equations using partial pivoting by the Gauss elimination method. 2x + 3y +x = 4x + 2y + 3z = 4x + y + z = 0
[4 marks]Solve the following systems of equations using Gauss Jacobi method. 6x + 2y z = X + 5y +4z = 27
[4 marks]Use the Gauss-Seidal method to solve 6x + y + z = 105 4x + 8y + 3z = 155 5x + 4y 10z = 65
[7 marks]Write relation between and E, and E.
[3 marks]Determine the polynomial by Newton’s forward difference formula from the following table. x 0 1 2 3 4 y 10 8 8 4 10 40
[5 marks]Employ Stirling’s formula to compute y (35) from the following table. x 20 30 40 50 y 512 439 346 243
[7 marks]Write relation between and E, and E.
[3 marks]Using Langrange’s interpolation formula , find the value of y when x= 10 from the following table X 5 6 9 11 Y 12 13 14 16
[4 marks]Using Newton’s divided differences foemula, compute f(0.5)from the following table.1 X 10 11 13 17 F(x) 2.3026 2.3989 2.5649 2.8332
[7 marks]Fit a straight line to the following data. X 1 2 3 4 6 Y 2.4 3 3.6 4 5
[6 marks]State Trapezoidal rule with n = 10 and evaluate .
[4 marks]Find the value y for y’ = x + y , y(0) = 1 when x= 0.1 , 0.2 with step size h = 0.05.
[7 marks]Fit a straight line to the following data. X 0 1 2 3 Y 1 1.8 3.3 4.5 6.3
[4 marks]Using Simpsons 1/3 rule with n = 10 and evaluate .
[4 marks]Given that y= 1.3 and x = 1, and y’ = 3x + y. Use the second order Runge- Kutta method to approximate y when x= 1.2. Use step size of x = 0.1.
[7 marks]Calculate the mean for the following frequency distribution. Class 0-8 8-16 16-24 24-32 32-40 40-48 Frequency 8 7 16 24 15
[7 marks]Calculate the first four movement of the following data. X 0 1 2 3 4 5 6 7 F 5 10 15 20 25 30 15 10
[5 marks]Calculate the regression coefficient and find two line of regression from the following data. X 57 58 59 59 60 61 62 64 Y 67 68 65 68 72 72 69 71
[7 marks]Calculate the arithmetic mean of the following marks obtained by students
[3 marks]Find the first four movements of the following data about the assumed mean 25 and actual mean. Class limit 0-10 10-20 20-30 30-40 Frequency 1 3 4
[2 marks]Following data represents rainfall (x) and yield of paddy per hectare (y) in a particular area. Find the linear regression of x on y. X 113 102 95 120 140 130 125 Y 1.8 1.5 1.3 1.9 1.1 2.0 1.7
[7 marks]