If the number a = 3.141592 is approximated by 3.14, find absolute error, relative error and percentage error.
[3 marks]Write an Algorithm for Newton-Raphson method.
[4 marks]Derive secant method. Use it to find a real root between 0 and 1 of the equation xex − 1 = 0, correct up to three decimal places.
[7 marks]Evaluate ∫ 0.6 e−x2 dx using Simpson’s 1/3 rule for n = 6.03
[ 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]Find all the roots of x3 −2x2 +x −2 = 0 using Bairstow’s method up to second iteration with p = q = 0.00
[7 marks]Using cubic spline, find y(0.5) and y’(1), given M = M = x 0 1 y −5 −4
[3 marks]Find a real root of the equation x3 −x−1 = 0 in the interval (1, 2) by the iteration method. Correct up to three decimal places.
[3 marks]Use Lagrange formula to find f(2) from the following table: x −1 0 2 f(x) 8 3 1
[12 marks]Apply Budan’s theorem to find the number of roots of the equation x5 +x4 −4x3 −3x2 +3x +1 = 0 in the intervals [−2,−1], [−1,0], [0,1] and [1, 2].
[7 marks]Explain ill conditional system with example.
[3 marks]Use Newton’s divided difference formula to determine f(9) for the following data: x 5 7 11 13 17 f(x) 150 392 1452 2366 52021
[4 marks]Fit a second degree parabola using least squares method to the following data: x 1 2 3 4 y 5 12 26 60 97 Also, estimate y at x = 6.
[5 marks]3 Evaluate ∫ f(x)dx from the following table using Simpson’s 3/8 rule:0 x 0 0.5 1 1.5 2 2.5 f(x) 1 0.6667 0.5 0.4 0.3333 0.2857 0.25
[3 marks]Develop a Cprogram for Trapezoidal rule.
[4 marks]dy Solve = x +y using Runge-Kutta method of order four, where y(0) = 1, with dx x = 0 to x = 0.2. Take ℎ = 0.1.
[7 marks]The coefficient of correlation between two variables Xand Yis 0.48. The covariance is 36. The variance of Xis 16. Find the standard deviation of Y.
[3 marks]Write an Algorithm for Gauss elimination method.
[4 marks]State diagonal dominance property. Solve the following system by Gauss-Seidel method correct to three decimal places: 2x +y+54z = 110; 27x +6y−z = 85; 6x +15y+2z = 72
[7 marks]Calculate the correlation coefficient between x and y using the following data: x 1 4 9 12 15 19 y 4 7 11 14 16
[20 marks]From the following data, find the number of items n: r = 0.5, ∑(x−x)(y−y) = 120, 𝜎 = 8, ∑(x−x)2 = 90 Y
[4 marks]Define central moments. Calculate the first four moments from the following data: x 0 1 2 3 4 5 6 7 f 1 8 28 56 70 56 28 8 1
[8 marks]Calculate the 3-yearly moving averages of the following data: Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 Sales (millions of rupees)
[3 marks]Find the standard deviation for the following distribution: Age 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of Members
[4 marks]Obtain the line of regression of monthly sales(Y) on advertisement expenditure(X) and estimate the monthly sales when the company will spend Rs. 50,000 on advertisement, if the data on Yand Xare as follows: Y(in lac) 74 76 60 68 79 70 71 94 X (in thousand)
[7 marks]