Find the Taylor Polynomial of Order 3 Generated by F $$f ( x ) = \frac { 1 } { 5 - x } , a = 1$$

question 266

Multiple Choice

Find the Taylor polynomial of order 3 generated by f at a.
- $$f ( x ) = \frac { 1 } { 5 - x } , a = 1$$

• A) \(\mathrm { P } _ { 3 } ( \mathrm { x } ) = \frac { 1 } { 6 } - \frac { \mathrm { x } + 1 } { 36 } + \frac { ( \mathrm { x } + 1 ) ^ { 2 } } { 216 } - \frac { ( \mathrm { x } + 1 ) ^ { 3 } } { 1296 }\)
• B) \(P _ { 3 } ( x ) = \frac { 1 } { 6 } - \frac { x - 1 } { 36 } + \frac { ( x - 1 ) ^ { 2 } } { 216 } - \frac { ( x - 1 ) ^ { 3 } } { 1296 }\)
• C) \(\mathrm { P } _ { 3 } ( \mathrm { x } ) = \frac { 1 } { 4 } - \frac { \mathrm { x } + 1 } { 16 } + \frac { ( \mathrm { x } + 1 ) ^ { 2 } } { 64 } - \frac { ( \mathrm { x } + 1 ) ^ { 3 } } { 256 }\)
• D) \(P _ { 3 } ( x ) = \frac { 1 } { 4 } - \frac { x - 1 } { 16 } + \frac { ( x - 1 ) ^ { 2 } } { 64 } - \frac { ( x - 1 ) ^ { 3 } } { 256 }\)

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