Here is one, have fun with the simplicity
First I let
I then made the sub, let
So we have that
So by subbing we have
Now there are a few ways this could have been done, but the easiest is the Root/Ratio laws test trick
which then by termwise division gives
For our second limit
multiplying by the conjugate gives
Now by breaking it up we get
now seeing that
Grouping we get
So then we have that
I've got a question for
Assuming that x tends to 0 from the right (>0), , while .
So we can neglect 3x with regard to
Therefore, the limit is
Also, I think you should be patient, we're not all in the same GMT and we're not as available as you are. So if no one answers within 2 hours, it's not a catastrophe...
As for thse second one
Yes it isSo if no one answers within 2 hours, it's not a catastrophe...