limit problem

[Guest]

I have this limit problem, that i am struggling with: find the limit ((x-1)*(x+2))/(x-3)^2, as x approaches -1.

I keep coming up with:

(1/16)(x)(1) - (1/16) which doesnt look right can anyone help?

Thanks very much

 

[tkhunny]

limit ((x-1)*(x+2))/(x-3)^2, as x approaches -1

You can try it out with algebra. Pick a small positive number, really small, say "M".

What does it look like moving in from the high side?
-1+M isn't quite -1
(((-1+M)-1)*((-1+M)+2))/((-1+M)-3)^2 Simplifies to (M^2 - M - 2)/(M^2 - 8*M + 16)
What happens to that as M gets smaller and smaller? (As M approaches zero)?

How about the other side?
-1-M isn't quite -1
(((-1-M)-1)*((-1-M)+2))/((-1-M)-3)^2 Simplifies to (M^2 + M - 2)/(M^2 + 8*M + 16).
What happens to that as M gets smaller and smaller? (As M approaches zero)?

Just one way to go about it.

 

[Lizzie]

If you have a graphing calculator...

1)Put the equation in [y=]

2)Push [tblset]

3)Set "Indpnt" to "Ask"

4)Push

5)Put in values very close to 3, such as 2.9 or 3.01

This should tell you the answer. :wink: