Find the Third Degree Taylor Polynomial Centered At $c = 1$

question 153

Multiple Choice

Find the third degree Taylor polynomial centered at $c = 1$ for the function. $$f ( x ) = \sqrt { x }$$

• A) \(1 + \frac { 1 } { 2 } ( x + 1 ) - \frac { 1 } { 8 } ( x - 1 ) ^ { 2 } + \frac { 1 } { 16 } ( x + 1 ) ^ { 3 }\)
• B) \(1 + \frac { 1 } { 2 } ( x - 1 ) + \frac { 1 } { 8 } ( x - 1 ) ^ { 2 } - \frac { 1 } { 16 } ( x - 1 ) ^ { 3 }\)
• C) \(1 + \frac { 1 } { 2 } ( x - 1 ) - \frac { 1 } { 8 } ( x - 1 ) ^ { 2 } + \frac { 1 } { 16 } ( x - 1 ) ^ { 3 }\)
• D) \(1 + \frac { 1 } { 2 } ( x - 1 ) - \frac { 1 } { 8 } ( x - 1 ) ^ { 2 } - \frac { 1 } { 16 } ( x - 1 ) ^ { 3 }\)
• E) \(1 + \frac { 1 } { 2 } ( x + 1 ) + \frac { 1 } { 8 } ( x - 1 ) ^ { 2 } - \frac { 1 } { 16 } ( x + 1 ) ^ { 3 }\)

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