Since the original limit is finite, what must
be?
If then find
This has me pretty stumped. Since the denominator is zero at x=1, I can't use limit of quotient is the quotient of the limits. My only other thought was to figure out f(x), which should be a polynomial where f(x)-8 has a factor of 1-x, but I can't figure out what that would be.
To do this problem, we're going to find out what f(x) is, and then take the limit. To find f(x), we do this:
We know that has to have an in it. We also know that the other factor must be equal to 10, when we plug in a 1 for x. Therefore, the other factor must be
If we FOIL, we have:
Now we separate the -8 from the mix:
So we have:
When we plug in 1, we get our answer: 8
I hope this helps!
-Nathan
I figured there was another way to solve this problem, but to be honest, I did not know the exact method, so I used a way that I knew would work.I'm not sure I agree with this approach. f(x) doesn't even have to be defined in order to solve this problem.
Sometimes the front door is locked, so you need to break through the window
-Nathan
No, we don't know that because we don't know that f is a polynomial.
We also know that the other factor must be equal to 10, when we plug in a 1 for x. Therefore, the other factor must be
If we FOIL, we have:
Now we separate the -8 from the mix:
So we have:
When we plug in 1, we get our answer: 8
I hope this helps!
-Nathan
Oops, I apologize, I read the problem and started thinking polynomial:
I should have thought it through more. Thanks for the correction!My only other thought was to figure out f(x), which should be a polynomial where f(x)-8 has a factor of 1-x, but I can't figure out what that would be.
-Nathan