Use the Alternating Series Estimation Theorem or Taylor's Inequality to Estimate

question 131

Short Answer

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of $x$ for which the given approximation is accurate to within the stated error.
$\cos x \approx 1 - \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 24 } \quad \mid$ error $\mid < 0.08$
Write $a$ such that $- a < x < a$ .

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Definitions:

Deferred Imitation

The cognitive process where a person, often a child, observes and replicates others' actions at a later time, without the model being present.

Explicit Memory

A type of long-term memory involving conscious recollection of factual information, previous experiences, and concepts.

Child-Directed Speech

A type of speech characterized by exaggerated expressions, simpler vocabulary, and clearer pronunciation, used by adults when talking to young children.

Underextension

A cognitive error in language acquisition where a child applies a word in a narrower way than it is usually applied, failing to include objects or events that are part of the category.