Suppose that ai and bi are coe?cients in the Taylor polynomials of f and g respective (at 0).
Thus ai = f(to the i derivative) (0)/(i!) and bi = g( to the i derivative) (0)/(i!). Find the Taylor coe?cients ci of the following
functions (at 0) in terms of the ai and bi .
(i) f + g
(ii) f - g
(iii) f'
(iv) (f)(g)
(v) h(x) = (the integral from 0 to x) f(t) dt
Sorry about my limited notation, but I'm not even sure how to get started. If someone could give me a hint in the right direction that would be great.
Thus ai = f(to the i derivative) (0)/(i!) and bi = g( to the i derivative) (0)/(i!). Find the Taylor coe?cients ci of the following
functions (at 0) in terms of the ai and bi .
(i) f + g
(ii) f - g
(iii) f'
(iv) (f)(g)
(v) h(x) = (the integral from 0 to x) f(t) dt
Sorry about my limited notation, but I'm not even sure how to get started. If someone could give me a hint in the right direction that would be great.
