If this is a quiz are you allowed to ask for help?
This is the last problem on a take home quiz I was given. I keep staring at it, but I'm not really even sure how to start.
Determine all possible values of and if
I've done some searching, and found 2 instances of a similar problem:
Yahoo! Canada Answers - Find Numbers a and b for a limit?
Find numbers a and b? - Yahoo! Answers
In both of those problems, the denominator in the limit is only X, so they state that as x->0, the numberator must be equal to zero as well.
Ok, so
in both the examples that I have found, the person working it out would put in a 0 for a at this point. Ok, but If I do that,
or
That cannot be broken up anymore. In the examples, after finding b using this method, they use it to find other values. But without a way to isolate b I'm stuck.
Thanks in advance for any help.
So I've kept working at it and I've determined that a can = -1
from there I plugged that value of a into the limit:
and because that is a form, I applied L'Hospitals rule:
I know that if then the limit equals 1, but I'm not sure if the rule applies to multiples (ie: ?).
If it does hold true then b would be equal to 36.
Edit: just tried it and it does seem to hold true (I just dot remember seeing it anywhere).
So, A = -1 B = 36
Right, I know but .
I found this two ways, the first by pluging in 36 before applying L'Hospitals rule a second time
Wolfram Alpha
and second, after using the rule a second time I get:
in which
The question implies there are many possible values (or maybe thats just the way I read it?), where might I go from here?