Newton-Raphson Methods-QUIZ-1

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 are ways to verify whether there is a root in the interval [a, b] for a continuous function f(x) except

• f(a) < 0 and f(b) > 0

• f(a) x f(b) < 0

• f(a) x f(b) > 0

• The sign for f(a) and f(b) changes

The Newton Raphson method fails if __________

• f’(x0)=0

• f’’(x0)=0

• f(x0)=0

• f’’’(x0)=0

Using Newton-Raphson method, find the first root of the equation sin x = 1 - x starting with a₀=0

• 0.511

• 0.500

• 0.555

• -0.500

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

• Rolle's Theorem

• Extreme Value Theorem

• Intermediate Value Theorem

• 2.13

• 2.11

• 2.09

• 2.15

• 4.3

• 3.4

• 4.2

• 4.13

• 0.306

• 0.739

• 1.694

• 2.306

• A

• B

• C

• D

• A

• B

• C

• D