What are the answer for your these questions?
1 answer:
You might be interested in
First note that if 
, you have
Now, you're looking for
such that for any 
, you have
Note that you can divide through the left side of the
inequality by 
once more:
So it follows that you need to find an appropriate
that will guarantee
For the moment, let's fix
. Then by this assumption, we have
From this we get
where the upper bound is what we care about. With this assumption, we then get that
which suggests that can be taken to be either the smaller of 1 or 
, or 
, to guarantee that the function gets arbitrarily close to -8.
Now, you're looking for
Note that you can divide through the left side of the
So it follows that you need to find an appropriate
For the moment, let's fix
From this we get
where the upper bound is what we care about. With this assumption, we then get that
which suggests that