Is it true that if f(x) < g(x) for all x ∈ (c-ε , c+ε ) and that lim x -> c f(x) and lim x-> c g(x) both exists that lim x->c f(x)< lim x->c g(x)?
1 Answer
Mar 14, 2016
No, it is not true. The inequality in the conclusion need not be strict.
Explanation:
Take
In this case, we have
What is true is that under the conditions given, we always have