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2 D 30561

Section B

Answer any number of questions.
Each question carries 5 marks.
Ceiling is 30 marks.

13. Approximate the root of the function f(x) =cosx-x=0 using Newton’s method with py = 1/4.
14. Given / (2) = 5, f (2.5) = 6. Evaluate f (2.2) using Lagrange’s Method.
15. Using Newton’s divided difference interpolation formula evaluate / (3) from the following table :

x इ 1 2 4 5 6

y : 14 15 5 6 19

16. Use Newton’s forward-difference formula to approximate the derivative of f(x)=Inx at x) =1.8

using % - 0.01, % = 0.05 and A = 0.01 and determine bounds for the approximation errors.

17. The values for f(x)=xe* are given. Use Three-point end point formula to approximate /" (2.0)
with A = 0.1, -0.1:
3 ॥ 1.8 1.9 2 2.1 2.2

xe* $ 10.889365 12.703199 14.778112 17.148957 19.855030
18. Approximate the integral 42८८ using Trapezoidal Rule.

19. Use Euler Method to approximate the solution of the initial value problem
y'=1+(t-y),2
Section C

Answer any one question.
The question carries 10 marks.
Maximum marks 10.

20. Find a positive root of the equation f (x) = xe* —1 correct to 3 decimal places using Bisection Method.

21. Use the Midpoint method with N = 10, A = 0.2, t= 0.27, and 2८0 = 0.5 to approximate the solution

1० +” = + -{2 +1, 0 < ६ < 2, (0) = 0.5 .

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