Solve Limit: Find \lim_{n\rightarrow +2} {f(x)}

[maxitis]

I have the limit:
$$\lim_{x\rightarrow +2} {\frac{f(x)-5}{x-2}}=5$$
And i want to find the:
$$\lim_{n\rightarrow +2} {f(x)}$$
Can i say that $f(x)-5=5*(x-2)$
And then find the limit?
Thank you

 

[voko]

There is some confusion between n and x. Fix that. Then observe that as x (or n) goes to 2, the denominator goes to zero.

 

[maxitis]

And why is that a problem?
Both parts will be equal to 0.

 

[voko]

Because that would prevent you from using the formula you wanted.

But think about it. You have a finite limit of a ratio, whose denominator goes to zero. What can be said about the limit of its numerator in this case?

 

[HallsofIvy]

Yes, the denominator goes to 0. So what must the numerator go to in order that a limit exist?

 

[HallsofIvy]

I have the limit:
$$\lim_{x\rightarrow +2} {\frac{f(x)-5}{x-2}}=5$$
And i want to find the:
$$\lim_{n\rightarrow +2} {f(x)}$$
Can i say that $f(x)-5=5*(x-2)$
And then find the limit?
Thank you

No, because there are, in fact, an infinite number of possible functions, f. f(x)= 5(x- 2)+5 is just one of them.

Yes, the denominator goes to 0. So what must the numerator go to in order that a limit exist?

 

[maxitis]

The numerator should be zero.
So we have: $f(2)-5=0$ Am i right?

Something about before,
Why you said that there are infinite number of functions f that can satisfy that limit?
One is $f(x)=5(x-1)$, can you give me another example?
Thank you