# Solving a limit help

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

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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.

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

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

HallsofIvy
Homework Helper
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?

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

One is $f(x)=5(x-1)$, can you give me another example?