Provide an Appropriate Response $\tan x = x + \frac { x ^ { 3 } } { 3 } + \frac { 2 x ^ { 5 } } { 15 } + \frac { 17 x ^ { 7 } } { 315 } + \ldots$

question 80

Multiple Choice

Provide an appropriate response.
-Use the fact that $\tan x = x + \frac { x ^ { 3 } } { 3 } + \frac { 2 x ^ { 5 } } { 15 } + \frac { 17 x ^ { 7 } } { 315 } + \ldots$ for $| x | < \frac { \pi } { 2 }$ to find the first four terms of the series for ln(cos x) .

• A) \(- \left( 1 + x ^ { 2 } + \frac { 2 x ^ { 4 } } { 3 } + \frac { 17 x ^ { 6 } } { 45 } + \ldots \right)\)
• B) \(1 + x ^ { 2 } + \frac { 2 x ^ { 4 } } { 3 } + \frac { 17 x ^ { 6 } } { 45 } + \ldots\)
• C) \(\frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 12 } + \frac { x ^ { 6 } } { 45 } + \frac { 17 x ^ { 8 } } { 2520 } + \ldots\)
• D) \(- \left( \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 12 } + \frac { x ^ { 6 } } { 45 } + \frac { 17 x ^ { 8 } } { 2520 } + \ldots \right)\)

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