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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