Provide an Appropriate Response $x$ Can $\sin x$ Be Replaced By $x - \frac { x ^ { 3 } } { 6 } + \frac { x ^ { 5 } } { 120 }$

question 11

Multiple Choice

Provide an appropriate response.
-For approximately what values of $x$ can $\sin x$ be replaced by $x - \frac { x ^ { 3 } } { 6 } + \frac { x ^ { 5 } } { 120 }$ with an error of magnitude no greater than $5 \times 10 ^ { - 6 } ?$

• A) \(| x | < 0.59106\)
• B) \(| x | < 0.45942\)
• C) \(| x | < 0.54146\)
• D) \(| x | < 0.40357\)

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Definitions:

Precipitation

Any kind of water, either as a liquid or a solid, that drops from the clouds and lands on the Earth, covering types like rain, snow, sleet, and hail.

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Concentrations of gold found in sedimentary deposits, formed by gravity separation during sedimentary processes.

Caldera

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Weathered

The breakdown of rocks, soils, and minerals through contact with the Earth's atmosphere, water, and biological organisms.