NRI INSTITUTE OF TECHNOLOGY Visadala Road, Perecherla (P.O), Guntur District Subject: MM Marks : 15 I B. Tech I Semester I Mid Question Paper Each question carries equal marks: UNIT – I 1. a) Find the positive real root of the equation x 3 4 x 9 0 by bisection method correct to 3 places of decimal places. b) Find a real root of the equation by using bisection method cos 2x x 0 . 2. a) Find a positive root of the equation by Iteration method 2x 3 cos x . b) Find approximate value of the real root of x log 10 x 1.2 using third approximation by false position method. 3. a) Find approximate value of the real root of xe x 2 using Regula-Falsi method.. b) Find the real root of the equations x 3 x 2 0 correct to three decimal places by Newton - Raphson method. 4. a) Using Newton-Raphson method, find 23 . b) Using Iteration method find a root of equation x 3 x 10 0 perform 5 iterations using x0 0. 5. a) Using Newton-Raphson Method find Reciprocal of a number. b) Derive a formula to find the cube root of N using Newton-Raphson Method hence find the cube root of 15. UNIT – II 1 6.a) Evaluate f x if f x 2 at h=1. x 5x 6 b) Verify that the value of y when x=10 is 920 of y x 3 x 2 x 10 and only six values of y corresponding to 1,2,3,4,5,6 are used. 7.a) Find the missing term in the following: X logx 100 2.0000 101 2.0043 102 - 103 2.0128 104 2.0170 b) Prove that 2 2 E 1 8.a)The values of f(x) for x=0,1,2,……,6 are given by x 0 1 2 3 4 5 6 F(x) 1 3 11 31 69 131 223 Estimate the value of f(3.4) using only four of the given values by using Newton’s forward. x b) Certain values of x and log 10 are (300, 2.4771), (304, 2.4829), (305, 2.4843), (307, 2.4871). 301 Find log 10 9.a) Apply Gauss’s forward formula to find the value of u 9 , if u 0 14 , u4 24 u8 32 u12 35 u16 40 . b) Prove that 1 2 2 1 2 2 10.a) Given the values x 3 5 7 9 11 f(x) 6 24 58 108 74 Using Lagrange’s formula for interpolation find the value of f(6). b) Given u1=22, u2=30, u4=82, u7=106, u8=206, find u6. Using Lagrange’s formula for interpolation UNIT – III 11. Apply Taylor’s method to obtain approximate value of y(1.1) and y(1.2) correct to three 1 3 decimal places for the differential equation y xy , y 1 1 12. Solve by Euler’s method, y ' x y , y(0) = 1 and find y(0.3) taking step side h = 0.1 Compare the result obtained by this method with the result obtained by analytical method. dy xy y 2 , y 0 1 for y0.1, y0.2. 13. Use Runge-kutta method to solve dx dy x 2 y 2 , y 0 1 by using Picard’s method 14. Solve dx 15. Compute y at y = 1.5 in steps of 0.25 by Euler’s modified method given y ' xy 2, y1 1 ' ***********