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Newton-Raphson Methods-QUIZ-1

Authored by Chitra V

Mathematics

University

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Newton-Raphson Methods-QUIZ-1
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11 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The iteration formula for Newton-Raphson method is

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

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

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

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

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The Newton Raphson method fails if __________

f’(x0)=0

f’’(x0)=0

f(x0)=0

f’’’(x0)=0

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

Rolle's Theorem

Extreme Value Theorem

Intermediate Value Theorem

6.

MULTIPLE CHOICE QUESTION

15 mins • 5 pts

2.13

2.11

2.09

2.15

7.

MULTIPLE CHOICE QUESTION

15 mins • 5 pts

Media Image

4.3

3.4

4.2

4.13

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