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Use a Symbolic Differentiation Utility to Find the Taylor Polynomials f(x)=11+x2f ( x ) = \frac { 1 } { 1 + x ^ { 2 } }

Question 4

Multiple Choice

Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero) of degrees (a) 2, (b) 4, (c) 6, (d) 8. f(x) =11+x2f ( x ) = \frac { 1 } { 1 + x ^ { 2 } }


A) S2(x) =1−x2,S4(x) =1−x2+x4,S6(x) =1−x2+x4−x6,S8(x) =1−x2+x4−x6+x8S _ { 2 } ( x ) = 1 - x ^ { 2 } , S _ { 4 } ( x ) = 1 - x ^ { 2 } + x ^ { 4 } , S _ { 6 } ( x ) = 1 - x ^ { 2 } + x ^ { 4 } - x ^ { 6 } , S _ { 8 } ( x ) = 1 - x ^ { 2 } + x ^ { 4 } - x ^ { 6 } + x ^ { 8 }
B) S2(x) =1+x2,S4(x) =1+x2+x4,S6(x) =1+x2+x4+x6,S8(x) =1+x2+x4+x6+x8S _ { 2 } ( x ) = 1 + x ^ { 2 } , S _ { 4 } ( x ) = 1 + x ^ { 2 } + x ^ { 4 } , S _ { 6 } ( x ) = 1 + x ^ { 2 } + x ^ { 4 } + x ^ { 6 } , S _ { 8 } ( x ) = 1 + x ^ { 2 } + x ^ { 4 } + x ^ { 6 } + x ^ { 8 }
C) S2(x) =1−x2,S4(x) =1−x2−x4,S6(x) =1−x2−x4−x6,S8(x) =1−x2−x4−x6−x8S _ { 2 } ( x ) = 1 - x ^ { 2 } , S _ { 4 } ( x ) = 1 - x ^ { 2 } - x ^ { 4 } , S _ { 6 } ( x ) = 1 - x ^ { 2 } - x ^ { 4 } - x ^ { 6 } , S _ { 8 } ( x ) = 1 - x ^ { 2 } - x ^ { 4 } - x ^ { 6 } - x ^ { 8 }
D) S2(x) =1+x2,S4(x) =1+x2−x4,S6(x) =1+x2−x4+x6,S8(x) =1+x2−x4+x6−x8S _ { 2 } ( x ) = 1 + x ^ { 2 } , S _ { 4 } ( x ) = 1 + x ^ { 2 } - x ^ { 4 } , S _ { 6 } ( x ) = 1 + x ^ { 2 } - x ^ { 4 } + x ^ { 6 } , S _ { 8 } ( x ) = 1 + x ^ { 2 } - x ^ { 4 } + x ^ { 6 } - x ^ { 8 }
E) S2(x) =1−x2,S4(x) =1−x2+x4,S6(x) =1−x2+x4+x6,S8(x) =1−x2+x4+x6+x8S _ { 2 } ( x ) = 1 - x ^ { 2 } , S _ { 4 } ( x ) = 1 - x ^ { 2 } + x ^ { 4 } , S _ { 6 } ( x ) = 1 - x ^ { 2 } + x ^ { 4 } + x ^ { 6 } , S _ { 8 } ( x ) = 1 - x ^ { 2 } + x ^ { 4 } + x ^ { 6 } + x ^ { 8 }

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