Methods

Q.

Find and correct the errors in the mathematical statement $\frac{(3x^2+1)}{3x^2}=1+1=2$

Q. A numerical solution of the equation can be obtained using Newton- Raphson method

$f\left(x\right)=2\sqrt{x}+3x-6=0$

If the starting value is $x$ = 3 for the first iteration, the value of $x$ that is to be used in the next step is

1. 0.298
2. 2.385
3. 1.192
4. 0.596

Q. Solve the equation $x=e^{-x}$ using Newton-Raphson method. Starting with an initial guess values $x_0=0$, the value of x after first iteration is .

1. -0.050
2. -1
3. 0.50
4. 1

Q. Only one of the real roots of $f\left(x\right)=x^6-x-1$ lies in the interval $1\le x\le 2$ and bisection method is used to find its value. For achieving an accurancy of $0.001,$ the required minimum number of iteration is

1. 10

Q. Starting from $x_0=1$, one step of Newton-Raphson method in solving the equation $2x^3+5x-8=0$ gives the next value $\left(x_1\right)$ as

1. $\frac{5}{6}$
2. $\frac{11}{12}$
3. $\frac{6}{3}$
4. $\frac{12}{11}$

Q. The Newton-Raphson method formula for finding the square root of a real number N from the equation $x^2-N=0$ is

1. $x_{i+1}=\frac{5x_i}{2}$
2. $x_{i+1}=\frac{3x_i}{2}$
3. $x_{i+1}=\frac{1}{2}(x_i+\frac{N}{x_i^2})$
4. $x_{i+1}=\frac{1}{2}(x_i+\frac{N}{x_i})$