When do we know that a limit of a given function exists?

1 Answer
Andrea S.
Jun 13, 2017

In general you know that a given function has a limit only by determining its limit.

There are however some theorems ensuring a function has a limit under certain hypotheses, for example:

1) A monotonous function in an interval always has a limit

2) if f(x) <= g(x) <= h(x) and lim_(x->x_0) f(x) = lim_(x->x_0) h(x) = L then lim_(x->x_0) g(x) = L

3) If f(x) >= g(x) and lim_(x->x_0) g(x) = oo then lim_(x->x_0) f(x) = oo

4) If lim_(x->x_0) g(x) = 0 and f(x) is bounded, then lim_(x->x_0) f(x)g(x) = 0

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