Homework Help: Finding f(x) given limit

Please include parenthesis. Is it f(x)-8/x-1 or is it (f(x)-8)/(x-1). I'm assuming the latter. Also what is the given limit?

Edit, I see the limit now. Your notation was confusing. To answer your question, you know you can multiply limits, right? So lim x-> 1 (f(x)-8)/(x-1)=10, then you can multiply by a limit that you KNOW exists.

 

But even then, you can only know what the limit is at one point. You know nothing of the function. Is there more information?

 

Is the problem

find f(x)

or is the problem

find lim x-> 1 f(x)

 

So you can multiply limits, right? So you can multiply the given limit by something. What something would make it easier?

 

That's not what I meant at all. You can create an entirely NEW limit, then multiply it with your given limit, so long as the limit you create exists. What would simplify things?

 

"Make up a new limit for f(x)". No, you cannot "make up" a limit for f(x). That limit just is. But you CAN create a new function, g(x), such that lim x-> 1 g(x)=c, some constant (you create g(x), and from this you know what the constant is)

So then lim x-> 1 (f(x)-8)*g(x)/(x-1)=10*c

What g(x) would simplify this?

 

Huh? Would what address what? I think you might be overthinking this.

 

I have no idea where that equation came from.

 

Isn't that the limit you're given?

 

Also, you can't factor anything. x-1 is irreducible.

 

There is no point in this problem where you will factor anything. Also, there is no point in the problem where you will ever know what f(x) is.

Like I said, you need to multiply the limit you are given by another limit that you create.

 

I'll go one step further. FIRST you must multiply the limit you are given by another limit you create. Then you must add another limit to it. THEN you will be done. The tricky part is coming up with those two limits (but it'll click and make sense after the first one.).

 

So then lim x-> 1 (f(x)-8)*g(x)/(x-1)=10*c

What g(x) would simplify this?

This is the only thing you should be thinking about right now. What g(x) will make this easier? It won't solve it, there is another step coming, but what will simplify it? Also, what is the associated "c", the lim x->1 g(x)?

 

g(x) is a function. c is the limit as x->1 of g(x)

 

This is what I'm using.