Compute
Since for all
we have
for all . Since
, we have
by the squeeze theorem (Theorem 3.3 in Apostol).
Compute
Since for all
we have
for all . Since
, we have
by the squeeze theorem (Theorem 3.3 in Apostol).
You have a mistake here. When you multiply your first inequality by x you need to consider the sign of x.
Right. That’s why it is better to use the inequalities
.