Lemma.
for all constant values of
Proof. Let
be any positive number. Then we get:
as soon as
theorem.
The growth of the real exponential function
exceeds all power functions, i.e.
with
Proof. Since
, we obtain by using the lemma the result
Corollary 1.
Proof. According to the lemma we get
Corollary 2.
Proof. Change in the lemma
to
.
Corollary 3.
(Cf. limit of nth root of n.)
Proof. By corollary 2, we can write:
as
(see also theorem 2 in limit rules of functions).
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