Provide an Appropriate Response $x$ Can $\cos x$ Be Replaced By $1 - \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 24 }$

question 335

Multiple Choice

Provide an appropriate response.
-For approximately what values of $x$ can $\cos x$ be replaced by $1 - \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 24 }$ with an error of magnitude no greater than $5 \times 10 ^ { - 5 }$ ?

• A) \(| x | < 0.42628\)
• B) \(| x | < 0.51435\)
• C) \(| x | < 0.57462\)
• D) \(| x | < 0.35944\)

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Definitions:

Habituation

A psychological learning process wherein there is a decrease in response to a stimulus after being repeatedly exposed to it.

Acquisition Behavior

A behavioral psychology term referring to the process of learning new behaviors, often through conditioning.

Classical Conditioning

A learning process that occurs when two stimuli are repeatedly paired: a response which is at first elicited by the second stimulus is eventually elicited by the first stimulus alone.

Ivan Pavlov

A Russian physiologist known for his research on classical conditioning, demonstrating how organisms can learn to associate neutral stimuli with reflexive responses.