Use a Symbolic Differentiation Utility to Find the Fourth-Degree Taylor $f ( x ) = \frac { 1 } { \sqrt [ 3 ] { x + 1 } }$

question 52

Multiple Choice

Use a symbolic differentiation utility to find the fourth-degree Taylor polynomials (centred at zero) . $f ( x ) = \frac { 1 } { \sqrt [ 3 ] { x + 1 } }$

• A) \(S _ { 4 } ( x ) = 1 - \frac { x } { 3 } + \frac { 2 x ^ { 2 } } { 9 } - \frac { 14 x ^ { 3 } } { 81 } + \frac { 35 x ^ { 4 } } { 243 }\)
• B) \(S _ { 4 } ( x ) = 1 + \frac { x } { 3 } + \frac { 2 x ^ { 2 } } { 9 } + \frac { 14 x ^ { 3 } } { 81 } + \frac { 35 x ^ { 4 } } { 243 }\)
• C) \(S _ { 4 } ( x ) = 1 - \frac { x } { 3 } - \frac { 2 x ^ { 2 } } { 9 } - \frac { 14 x ^ { 3 } } { 81 } - \frac { 35 x ^ { 4 } } { 243 }\)
• D) \(S _ { 4 } ( x ) = 1 + \frac { x } { 3 } - \frac { 2 x ^ { 2 } } { 9 } + \frac { 14 x ^ { 3 } } { 81 } - \frac { 35 x ^ { 4 } } { 243 }\)
• E) \(S _ { 4 } ( x ) = 1 - \frac { x } { 3 } + \frac { 2 x ^ { 2 } } { 9 } + \frac { 14 x ^ { 3 } } { 81 } - \frac { 35 x ^ { 4 } } { 243 }\)

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