1)A function f(x) satisfies

f(1) = 3 , f'(1) = 1, f''(1) = 2, f'''(1) = -3, ...

What is the coefficient c2 in the Taylor series expansion of f(x)

c0 +c1(x-1) + c2(x-1)^2 + c3(x-1)^3 + ...?

2) For the function 1/(1+2x^2) find a power series representation about x=0. What is the coefficient of x^4 in this series?

3) Find the first coefficients of the MacLaurin series expansion

indefinite integral of (4+9x^2)^0.5 = C + c1x +c2x^3 + c3x^5 + ...

where C represents the constant of integration.

find c1, c2 and c3.