2. Suppose DC R and functions f: D→ R and g: DR. Suppose to is an accumulation point of D and lim f(x) = A all lim g(x)=B both exist (except in last part below). H-10 (a) Show that lim f(x) g(x) = AB, using the definition. HIHO (b) Show that lim f(x)g(x) = AB, using sequences. X-10 01 x (c) Give an example to show that lim f(x) g(x) may exist even though both lim f(x) and lim g(x) do not exist. HIO I-IO HIHO

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