Mathematics-3 question answer collection notes

Q.1 Express f(x)=x as a half range sine series in 0 < x < 2 Q.2 Obtain the Fourier series for the function f(x)=x2 in -Π < x < Π ( -Pai < x < Pai) Q.3 Find the Fourier sine transform of f(x) = 1 / x . Q. 4 : Find a root of the equation x³-4x-9=0 using bisection method correct to three decimal places. RGPV DEC 2018 Q. 5: Using Newton-Raphson method, find the real root of the equation 3x=cos x+1. RGPV DEC 2018 Q. 6: Find the cubic polynomial which takes the following values- RGPV DEC 2018 Q. 7 : By means of Newton's divided difference formula, find f(8) and f(9) from the following data- RGPV DEC 2018 Q. 8: Using Simpson's 1/3 rule, obtain by taking sevan ordinates. Compare it with exact values. RGPV DEC 2018 Q. 9 : Solve the following system by Gauss elimination method- 6x + 3y + 2z = 6 RGPV DEC 2018 Q. 10 : Solve the following system of equations using Gauss-Seidel method- 27x + 6y - z = 85 RGPV DEC 2018 Q. 11 : Using Lagrange's interpolation formula, find the cubic polynomial that takes the following values. RGPV DEC 2018 Q. 12 : Using Runge-Kutta method of fourth order solve the differential equation- dy / dx = xy for x = 1.2 RGPV DEC 2018 Q. 13 : Using Picard's method find y for x = 0.1 Given that RGPV DEC 2018 Q. 14 : Solve the given equation for y(1.1) using Taylor series method- RGPV DEC 2018 Q. 15 : Find the followings- (i) L{t^2 sin at} RGPV DEC 2018 Q. 16 : Using convolution theorem find L^-1 {1 / (s-1)(s+2)}. RGPV DEC 2018 Q. 17 : Using Laplace transform, solve equation (D² + 2D +1) y=t. Given that y(0) = -3, y(1) =1. RGPV DEC 2018 Q. 18 : Find the probability that at most 5 defective fuses will be found in a box of 200 fuses if experience shows that 2% of such fuses are defective. RGPV DEC 2018 Q. 19 : Find mean and variance of Binomial distribution. RGPV DEC 2018 Q. 20 : Find a root of following equation using bisection method correct to three places of decimal f(x)=x^3-3x-5. RGPV MAY 2019