to find the value of such that
some help here..
I'd be astonished if students at the level of l'Hospital had not been taught power series.
And if students have not been taught l'Hospital, I'd be totally astonished if they got these sorts of questions and were expected to use it .......
All too often using l'Hospital is just plain lazy. And often it cultivates a mindset that leads to its invalid use.
Using l'Hospital is like driving 50m to the convenience store instead of walking.