i'm having problem solving this one....
i'll be really grateful if you help me on this one
Uhm... I think it might be $\displaystyle -9-e^{3t} $ in the first box, $\displaystyle -(-9-e^{3t})-1 $ in the second,$\displaystyle -(-1)-1 $ in the third and $\displaystyle -(-1)+3\cos(-9t) $ in the last one. Not sure though...
If this is for WebWork, you could try these. If you have unlimited tries that is.
Obviously $\displaystyle f_1(t)=-9-e^{3t}$ goes in the first box, then what goes in the $\displaystyle (n+1) $th box is: $\displaystyle f_{n+1}(t)=-f_n(t)+g_{n+1}(t)$ where $\displaystyle g_n(t)$ is the function in the $\displaystyle n $th part of the function definition, so:
$\displaystyle g_1(t)=)=-9-e^{3t}$
$\displaystyle g_2(t)=-1$
$\displaystyle g_3(t)=-1$
$\displaystyle g_4(t)=3 \cos(-9t)$
CB