taylor-polynomials-1

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Question 8 (Taylor polynomials)

The Taylor series about 0 for the function

f(x) =( 9/16 + x)^ -1/2

is

f(x) =4/3-32/27x +128/81x^2-5120/2187x^3 +……, for – 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.

 

 

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