I've encountered some difficult problems in my textbook that I can't solve. Any help would be appreciated. This is not homework—I'm just looking to advance my knowledge, that's all.
Question 1: (SOLVED, but I still don't understand the general method for solving these kinds of problems)
For each , find a so that is true. What does this show?
(By the way, how do I get the absolute characters to extend all the way in LaTeX?) SOLVED: Use \left| and \right|
Question 2: (SOLVED, but I still don't understand the general method for solving these kinds of problems)
Show that when using the definition of limits.
This is what I've got so far:
As soon as we've chosen a , then we'll be able to find a so that
when .
Note:
Question 3: (SOLVED)
Is continuous for all ?
Is continuous for all ?
I need help with another limit.
This is what I've done so far.
If this is correct, then the question becomes; what can I do with:
Also, I've solved this one, but my solution seems a bit strange. Anyone have a better solution?
I used a substitution:
, when
So we have: