the limit x approaches 2 (x^2-4x+4)/(x-2) represents the derivative of a function f at a number a. what is f(x)? can someone help me start this one off?

Question

jigglypuff314 · Answer

factor the top and then you can cancel then plug

jdoe0001 · Answer

... not even sure what's being asked, doesn't look like is the limit though

jigglypuff314 · Answer

$$\lim_{x \rightarrow 2}\frac{ x ^{2}-4x+4 }{ x-2 }$$
x^2 - 4x + 4 = (x-2)(x-2)

anonymous · Answer

ok I get (x-2) is that f(x)?

jigglypuff314 · Answer

plug in what the limit approaches into x

anonymous · Answer

when I plug 2 in I would just get 0.

jigglypuff314 · Answer

yes

anonymous · Answer

so a=0?

jigglypuff314 · Answer

i suppose so

jdoe0001 · Answer

hmm

jdoe0001 · Answer

so it's 0.. I see it's indeed just the limit

anonymous · Answer

No i'm not looking for the limit I need to find f(x)

jdoe0001 · Answer

well... hmm the function "f" is the function given to the limit, so f(x) proper will be $\bf lim_{x \to 2}\color{red}{\cfrac{ x ^2-4x+4 }{ x-2 }}$  only

jdoe0001 · Answer

but I understood as f(x) as f(2) pretty much, I know the number "a" is 2

so I'd think for a function "f" f(x) as x goes to 2, will be f(2)

anonymous · Answer

so as a function f(x)=x-2

jdoe0001 · Answer

the simplified version, yes

in proper it should be without any  simplification because it has restrictions on the denominator

anonymous · Answer

thank you

jdoe0001 · Answer

yw