Provide an Appropriate Response $x$ Can $\tan ^ { - 1 } x$

question 203

Multiple Choice

Provide an appropriate response.
-For approximately what values of $x$ can $\tan ^ { - 1 } x$ be replaced by $x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 }$ with an error of magnitude no greater than $5 \times 10 ^ { - 8 }$ ?

• A) \(| x | < 0.11699\)
• B) \(| x | < 0.08182\)
• C) \(| x | < 0.11960\)
• D) \(| x | < 0.08395\)