1) let f(x) be a function with the following properties: i. f(0)=1
ii. For all integers n >= 0, the nth derivative, f^(n)(x)=(-1)^(n)a^(n)f(x), where a > 0 & a doesnt equal 0, in terms of a
A) write the first fur non zero terms and the general term of the power series of f(x) centered at zero, in terms of a

Answer(1)=c; expanded food and nutrition education program; answer(2)=a; elderly and those with health issues; answer(3)=nutrition program for the elderly;

The answer is    (d) 7/2======we have    we also  have an integral      notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum:     notice that for the piecewise function f, the function has the equationf(x) = x when x  ≤ 0. so for the integral  , f(x) = x so it changes into      for the piecewise function f, the function has the equationf(x) = x+1  when x  > 0. for the integral  , we have    therefore, back to our splitted integral:    

Its complicated if im correct its confused