Provide an Appropriate Response $\cot x = \frac { 1 } { x } - \left( \frac { x } { 3 } + \frac { x ^ { 3 } } { 45 } + \frac { 2 x ^ { 5 } } { 945 } + \ldots \right)$

question 354

Multiple Choice

Provide an appropriate response.
-Use the fact that $\cot x = \frac { 1 } { x } - \left( \frac { x } { 3 } + \frac { x ^ { 3 } } { 45 } + \frac { 2 x ^ { 5 } } { 945 } + \ldots \right)$ for $| x | < \pi$ to find the first four terms of the series for ln(sin $x$ ) .

• A) \(- \left( \frac { 1 } { x ^ { 2 } } + \frac { 1 } { 3 } + \frac { x ^ { 2 } } { 15 } + \frac { 2 x ^ { 4 } } { 189 } + \ldots \right)\)
• B) \(\frac { 1 } { x ^ { 2 } } + \frac { 1 } { 3 } + \frac { x ^ { 2 } } { 15 } + \frac { 2 x ^ { 4 } } { 189 } + \ldots\)
• C) \(\ln | x | - \left( \frac { x ^ { 2 } } { 6 } + \frac { x ^ { 4 } } { 180 } + \frac { x ^ { 6 } } { 2835 } + \ldots \right)\)
• D) \(- \ln | x | + \frac { x ^ { 2 } } { 6 } + \frac { x ^ { 4 } } { 180 } + \frac { x ^ { 6 } } { 2835 } + \ldots\)

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Definitions:

Americas

A collective term for the continents of North and South America, including the associated islands and regions therein.

Domestication

The process of adapting wild plants and animals for human use, such as for food, work, clothing, or companionship.

Reproductive Success

The relative production of fertile offspring by a genotype. In practical terms, the number of offspring produced by individual members of a population is tallied and compared to that of others.