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:

Downward-Sloping

Describes a line on a graph that decreases in height as it moves from left to right, indicating a negative relationship between two variables.

Inelastic Demand

A situation where the demand for a product does not significantly change with a change in the product's price, indicating that consumers are less sensitive to price changes.

Total Revenue

The total receipts from sales of a given quantity of goods or services. It is the total income of a business from its sales activity.

Price

The amount of money required to purchase something or the value that consumers are willing to exchange for a good or service.