Question

Show by means of an example that lim x-> a [f(x) + g(x)] may exist evn though neither lim x-> a f(x) adn lim x -> a g(x) exists.

Answer 1

For example f(x) is a negative g(x) plus some simple function.
g(x) = 1/ (x-a)
f(x) = (-1)/(x-a) + x