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Question 8 (Taylor polynomials)
The Taylor series about 0 for the function
f(x) =( 9/16 + x)^ -1/2
f(x) =4/3-32/27x +128/81x^2-5120/2187x^3 +â€¦â€¦, for â€“ 9/16 < x < 9/16 :
(a)Use differentiation to find the Taylor series about 0 for the function
g(x) = (9/16 + x)^-3/2,
Giving all terms up to the one in x^2, and calculating each coefficient as
an integer or a fraction.
(b) Use integration to find the Taylor series about 0 for the function
h(x) = (9/16 + x)^1/2;
giving all terms up to and including the one in x^4, and calculating each
coefficient as an integer or a fraction.