Given $f ( x ) = x ^ { 2 } - 3$

question 8

Multiple Choice

Given $f ( x ) = x ^ { 2 } - 3$ , use Newton's method to find the iterative formula for $x _ { n + 1 }$ .

• A) \(x _ { n + 1 } = x _ { n } + \frac { 1 } { 2 x _ { n } }\)
• B) \(x _ { n + 1 } = x _ { n } + \frac { 3 } { 2 x _ { n } }\)
• C) \(x _ { n + 1 } = \frac { x _ { n } } { 2 } - \frac { 3 } { 2 x _ { n } }\)
• D) \(x _ { n + 1 } = x _ { n } + \frac { 3 } { x _ { n } }\)
• E) \(x _ { n + 1 } = x _ { n } - \frac { 1 } { 2 x _ { n } }\)
• F) \(x _ { n + 1 } = x _ { n } - \frac { 3 } { 2 x _ { n } }\)
• G) \(x _ { n + 1 } = \frac { x _ { n } } { 2 } + \frac { 3 } { 2 x _ { n } }\)
• H)None of these

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Definitions:

Piaget

Jean Piaget was a Swiss psychologist known for his pioneering work in child development, particularly his theory of cognitive development that describes how children develop intellectually throughout the course of childhood.

Egocentric

Having or regarding oneself as the center of all interests and perspectives, often ignoring others' viewpoints.

Sky Is Blue

A statement describing the appearance of the Earth's sky in clear conditions due to the scattering of sunlight by the atmosphere.

Centration

A cognitive limitation in early childhood development where a child focuses only on one aspect of an object or situation, overlooking others.