problem with limits algebraicly

[spezialize]

i need to find the limit as x approaches 2...

(x^2-3x+2)/x-2

Can anyone point me in the right direction.. Thanks!

 

[pka]

(x<SUP>2</SUP>-3x+2)=(x−2)(x-1), thus for every x≠2, we have (x<SUP>2</SUP>-3x+2)/(x-2) = (x−1).
But as x approaches 2, x is simply ‘near’ two.
BUT NEVER EQUAL TO 2!.
Thus as for any x ‘near’ 2 we can use (x−1).
Now if x is ‘near’ 2 what value is (x−1) ‘near’?
That is the limit.

 

[stapel]

pka has given you a nice explanation of the limit for this exercise. I'd only like to add that you have seen this sort of thing before, back in algebra, and remembering what you did there might be helpful:

Remember when you were working with rational functions, graphing asymptotes and zeroes and such? And every once in a while you'd have one that graphed as a straight line, except for one little hole where the function wasn't defined. That's all you're dealing with here. You're just bringing new tools (that is, calculus) to the problem.

Eliz.

 

[spezialize]

I have never seen this in algebra before..