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02000M A202052001

1 if |x|<1

0 {|| > 1 Hence show (மர்‌

Find the Fourier Transform of f(x) =|

ಚ sinw 00 = ट
Solve using Laplace Transform: y" — 3y’ + 2y = 4 given y(0) = 2,y’(0) = 3

PART C (MODULES V AND VI)
Answer two full questions.

Using Lagrange’s interpolation formula, find a parabola of the form y = ax? +
bx + c passing through the points (0,0), (2,4) and (3,12)

Using Newton-Raphson Method, find the real root lying between 0 and 1 of
3x — cosx — 1= 0. (Correct to three decimal places)

Apply Lagrange’s interpolation formula to find y at x = 2 for the following values
for y = f(x). Given f(0) = —12,f(1) = 0, f (3) = 6 and f(4) = 12.

Solve by Gauss Elimination Method:

3x + 4y + 5z = 18, 2x -y+8z= 13, 5x — 2y + 72 = 20.
Evaluate | = ರಾ. using (i) Trapezoidal Rule (ii) Simpson’s = Rule (Take
h=1). Also find the value of the integral by actual integration.

Using Euler’s Method compute the value of y(0.1) given y’ =x +5 , (0) = 1

(Take h = 0.025)
Using Newton’s Interpolation Formula find f(1.2)and f (2.0) from the table.

Using Runge — Kutta Method of 4" order, find y(0.8) correct to four decimal

places if? = y—x? given y(0.6) = 1.7379 (Take h = 0.1)

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