Derive iterative formula for qth root using Newton-Raphson method.
[3 marks]Using bisection method, find a positive root of the equation f(x)=x – cosx= 0
[4 marks]Compute the appropriate value of f(7.5) by using suitable interpolation formula using the following data, x 3 4 5 6 7 f(x) 28 65 126 217 344 513
[8 marks]Evaluate fkkkkkkkk ] equation f9x0ff1 601 + x d x04 by taking h=1 using Simpson’s 1/3 rule.
[ marks]Write at least two differences between secant method and false method.
[3 marks]Using method of least squares, find the best fitting straight line to the given following data. x 1 2 3 4 f(x) 1 3 5 6
[5 marks]Obtain cubic splines approximation for the following data for the following data and hence compute f(1.5) X 1 2 f(x) -8 -1 18
[3 marks]Apply Budan’s theorem to the equation x4 −7x2 +6x−1=0to draw the inference about the roots in the interval (-2,-1).
[3 marks]Find square root and reciprocal of 8 correct up to four decimal places using Newton-Raphson’s Method.
[4 marks]Using Gauss Seidel method solve the following equations. Use (x, y, z) = (1,0,1) as the initial guess value. 12x+3y-5z=1 x+5y+3z=28 3x+7y+13z=76
[7 marks]Prove the following (1)1/2= +0.5 (2) =0.5E-1 +0.5
[3 marks]Employ Stirling’s formula to compute y(35) from the following table. x 20 30 40 50 f(x) 512 439 346 243
[4 marks]Find the roots of the2 x 3 − 2 x 2 + x − 2 = 0 using Lin-Bairstow’s method up to second iteration with p =q =000
[7 marks]3 1 Evalute dxwith n=6 by using Simpson’s 3/8 rule 1+x0
[3 marks]The following table gives the marks obtained by 50 students in mathematics. Find the median. Marks 0-10 10-20 20-30 30-40 40-50 No.of 16 12 18 3 1 Students
[4 marks]Using Euler’s method, find y (0.04) for the following initial value problem. y=y, y (0) = 1. Take step size as h= 0.01.
[7 marks]Write the formula for Runge-Kutta second order method.
[3 marks]Using Newton’s divided difference formula, compute f(10.5) from the following data. x 10 11 13 17 f(x) 2.3026 2.3979 2.5649 2.8332
[4 marks]Using improved Euler’s method, solve y+ 2xy2 = 0 with the initial condition y(0) = 1 and compute y(1) taking h= 0.2. Compare with exact solution.
[7 marks]Develop Cprogram for bisection method.
[3 marks]Adiscrete random variable Xhas the following probability distribution. X 0 1 2 3 4 F(X=x) 0 k 0.2 2k 0.3 2k (1) Find k (2) Compute P(X<3), P(X3), P(2<X<5), P(X4)
[5 marks]Find the correlation coefficient from the following data. X 1 2 3 4 5 6 Y 6 8 11 9 12 10
[14 marks]Discuss type of Regression.
[3 marks]The score of 12 students in their mathematics (X) and Statistics (Y) are as follows. Find the regression line of Yon X. X 2 3 4 4 5 6 6 7 7 8 10 Y 1 3 2 4 4 4 6 4 6 7 9
[10 marks]Using Milne’s method, solve y=1+y2 with y(0)=0, y(0.2)=0.2027, y(0.4)=0.4228, y(0.6)=0.6841.Compute y(0.8) and y(1).
[7 marks]