Numerical Methods II Odd 2021-2022

False Position method is used to solve

• quadratic equations

• system of linear equations

• eigen value problems

• nonlinear equations

Regula Falsi method is also known as ------

• Interval halving method

• Bolzano's method

• Method of False Position

• Newton method

The iteration formula for Newton-Raphson method is

• $x_{n+1}=x_n+\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

• $x_{n+1}=x_n-\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

• $x_{n+1}=x_n-\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

• $x_{n+1}=x_n+\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

The following graphs show the situations where Newton-Raphson method may not work, except

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What line is used to find the next iteration in Newton-Raphson method?

• Secant

• Normal

• Chord

• Tangent

In Newton-Raphson method, if we want to give our answer correct to 3 decimal places then we need to use how many decimal places in the calculation of the iterations?

• 3 decimal places

• 2 decimal places

• 4 decimal places

• any number of decimal places will do

If we want to give answer correct to 3 significant figures in the Newton-Raphson method, what the the stopping criteria?

• when two successive iterations give the same answers correct to 4 significant figures.

• when two successive iterations give the same answers correct to 2 significant figures.

• when two successive iterations give the same answers correct to 3 significant figures.

• when two successive iterations give the same answers correct to 1 significant figures.

Given that the equation  $2x^3-4x^2-1=0$  has a root in the interval [2, 3].  Using Newton-Raphson method, the root correct to 2 decimal places is

• 2.13

• 2.11

• 2.09

• 2.15

Which of the following iteration formula can not be derived from $x^2-6x+2=0$  

•  $x=\frac{x^2+2}{6}$  

•  $x=\sqrt{6x-2}$  

•  $x=6-\frac{2}{x}$  

•  $x=\sqrt{3\left(x-2\right)}$  

A theorem that guaranteed that there is at least a root in the interval is

• Rolle's Theorem

• Extreme Value Theorem

• Intermediate Value Theorem