Question

Taylor series:
f(x)=(1/16 +x)^(-1/4)
=2-8x+80x^2 -960x^3.....

and through differentiation g(x) = (1/16 +x)^(-5/4)
=32-640x+11520x^2

but i then need to integrate about 0, h(x)=(1/16 +x)^(3/4)
not really sure where to start out the integration one

Answer 1

Your Taylor expansion of f(x) is correct

I disagree with your derivative, it should be

(-1/4)((1/16 + x)^(-5/4)


why not just integrate

ʃ(1/16 +x)^(-1/4) dx
to get

(4/3)(1/16 + x)^(3/4) + C