(i) the functions $f_1(t)=t e^t $ and $f_2(t)=e^t$ are linearly independent on $(0,1)$.
(ii) $f_1(t)=t e^t $ and $f_2(t)=e^t$ are linearly dependent for every fixed $t\in (0,1)$.
I confused about this question. Part (i) and (ii) are really similar, but they are asking me two prove completely different things.
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