Let f,g: RR, and c E R. 1. Prove: if both lim f(x) and lim(f + g)(x) exist, then lim g(x) exists. x c х-с x c 2. If lim f(x) and lim(fg)(x) exist, is that true lim g(x) exists? Show your argument. x c х-с х-с

Identify the functions f and g such that lim f(x) does not exist, lim g(x) does not exist, but lim (f(x) + g(x)) does exist. Choose the appropriate functions. х — 6 6. g(x) = - x f(x) = f(x) g(x) x +6 g(x) -x - 6. f(x) = 6 f(x) x2 g(x) x2 f(x) 6. g(x) =

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2-lim,x-0 6х сot3x