The Newton-Raphson Algorithm Is Applied to Estimate a Zero of F(x)

question 84

Multiple Choice

The Newton-Raphson algorithm is applied to estimate a zero of f(x) with $x 0$ = 3. Which of the following statements is true?

• A) \(\mathrm { x } _ { 1 }\) = 3 - \(\frac { f ^ { \prime } ( 3 ) } { f ( 3 ) }\)
• B) \(\mathrm { x } _ { 1 }\) = 3 + \(\frac { f ^ { \prime } ( 3 ) } { f ( 3 ) }\)
• C) \(\mathrm { x } _ { 1 }\) = 3 - \(\frac { f ( 3 ) } { f ^ { \prime } ( 3 ) }\)
• D) \(\mathrm { x } _ { 1 }\) = \(\frac { f ^ { \prime } ( 3 ) } { f ( 3 ) }\)
• E) none of these

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Definitions:

Level of Significance

The threshold used in statistical hypothesis testing to decide whether to reject the null hypothesis, typically denoted by alpha (α) and set prior to conducting a test.

Measure of Performance

A metric used to evaluate the effectiveness, efficiency, or quality of a procedure, process, or activity.

Standard Deviation

An indicator of the spread or variability among a collection of numbers, reflecting the degree to which these numbers deviate from their average.

Hypotheses Testing

A method of statistical inference used to decide whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis.