PYQs

1) Apply Newton-Raphson method, to find a real root of transcendental equation $xlo{g}_{10}x=1.2$, correct to three decimal places.

[2019, 10M]

2) Write an algorithm in the form of a flow chart for Newton-Raphson method. Describe the cases of failure of this method.

[2017, 15M]

3) Apply Newton-Raphson method to determine a root of the equation $\cos x-x{e}^x=0$ correct up to four decimal places.

[2014, 10M]

4) Develop an algorithm for Newton-Raphson method to solve $f(x)=0$ starting with initial iterate $x_0$, $n$ be the number of iterations allowed, epsilon be the prescribed relative error and delta be the prescribed lower bound for $f^{\mathrm{\prime }}(x)$.

[2013, 20M]

5) Use Newton-Raphson method to find the real root of the equation $3x=\cos x+1$ correct to four decimal places.

[2012, 12M]

6) Find the positive root of the equation $10x{e}^{-x^2}-1=0$ correct up to 6 decimal places by using Newton-Raphson method. Carry out computations only for three iterations.

[2010, 12M]

7) Draw a flow chart for solving equation $F(x)=0$ correct to five decimal places by Newton-Raphson method.

[2008, 30M]

8) How many positive and negative roots of the equation $e^x-5\sin x=0$ exist? Find the smallest positive root correct to 3 decimals, using Newton-Raphson method.

[2004, 10M]

9) Find the positive root of the equation $2e^{-x}={\displaystyle \frac{1}{x+2}}+{\displaystyle \frac{1}{x+1}}$ using Newton-Raphson method correct to four decimal places. Also show that the following scheme has error of second order:
$x_{n+1}={\displaystyle \frac{1}{2}}{x}_n(1+{\displaystyle \frac{a}{x_n^2}})$.

[2003, 30M]