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Find the Taylor Polynomials (Centred at Zero) of Degree (A) f(x)=xx+1f ( x ) = \frac { x } { x + 1 }

Question 77

Multiple Choice

Find the Taylor polynomials (centred at zero) of degree (a) 1, (b) 2, (c) 3, and (d) 4. f(x) =xx+1f ( x ) = \frac { x } { x + 1 }


A) S1(x) =x,S2(x) =x−x2,S3(x) =x−x2+x3,S4(x) =x−x2+x3−x4S _ { 1 } ( x ) = x , S _ { 2 } ( x ) = x - x ^ { 2 } , S _ { 3 } ( x ) = x - x ^ { 2 } + x ^ { 3 } , S _ { 4 } ( x ) = x - x ^ { 2 } + x ^ { 3 } - x ^ { 4 }
B) S1(x) =x,S2(x) =x+x2,S3(x) =x+x2+x3,S4(x) =x+x2+x3+x4S _ { 1 } ( x ) = x , S _ { 2 } ( x ) = x + x ^ { 2 } , S _ { 3 } ( x ) = x + x ^ { 2 } + x ^ { 3 } , S _ { 4 } ( x ) = x + x ^ { 2 } + x ^ { 3 } + x ^ { 4 }
C) S1(x) =x,S2(x) =x−x2,S3(x) =x−x2−x3,S4(x) =x−x2−x3−x4S _ { 1 } ( x ) = x , S _ { 2 } ( x ) = x - x ^ { 2 } , S _ { 3 } ( x ) = x - x ^ { 2 } - x ^ { 3 } , S _ { 4 } ( x ) = x - x ^ { 2 } - x ^ { 3 } - x ^ { 4 }
D) S1(x) =x,S2(x) =x+x2,S3(x) =x+x2−x3,S4(x) =x+x2−x3+x4S _ { 1 } ( x ) = x , S _ { 2 } ( x ) = x + x ^ { 2 } , S _ { 3 } ( x ) = x + x ^ { 2 } - x ^ { 3 } , S _ { 4 } ( x ) = x + x ^ { 2 } - x ^ { 3 } + x ^ { 4 }
E) S1(x) =x,S2(x) =x+x2,S3(x) =x+x2−x3,S4(x) =x+x2+x3−x4S _ { 1 } ( x ) = x , S _ { 2 } ( x ) = x + x ^ { 2 } , S _ { 3 } ( x ) = x + x ^ { 2 } - x ^ { 3 } , S _ { 4 } ( x ) = x + x ^ { 2 } + x ^ { 3 } - x ^ { 4 }

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