Show by means of an example that lim x->a [f(x) + g(x)] may exist even though neither lim x->a f(x) nor lim x->a g(x) exists. How could I show this?
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One option is to take a function $\displaystyle f$, for which the limit at $\displaystyle x=a$ does not exist, and then take $\displaystyle g(x) = -f(x)$.