Find the Taylor Polynomial of Order 3 Generated by F $$f ( x ) = x ^ { 2 } + x + 1 , a = 5$$

question 428

Multiple Choice

Find the Taylor polynomial of order 3 generated by f at a.
- $$f ( x ) = x ^ { 2 } + x + 1 , a = 5$$

• A) \(P _ { 3 } ( x ) = 31 + 11 ( x - 5 ) + 11 ( x - 5 ) ^ { 2 } + 31 ( x - 5 ) ^ { 3 }\)
• B) \(P _ { 3 } ( x ) = 1 + 3 ( x - 5 ) + 3 ( x - 5 ) ^ { 2 } + ( x - 5 ) ^ { 3 }\)
• C) \(P _ { 3 } ( x ) = 6 + 11 ( x - 5 ) + 16 ( x - 5 ) ^ { 2 }\)
• D) \(P _ { 3 } ( x ) = 31 + 11 ( x - 5 ) + ( x - 5 ) ^ { 2 }\)

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