Question

Find limit x app 0 for (x-2)/(x^2-2x)

Answer 1

1/x so then can't have 0 in denominator so what then

Answer 2

factor the bottom then simplify.... then do direct substitution to find your limit.

Answer 3

Yes you get 1/x but you can't have zero in denominator so then what is the answer zero

Answer 4

It's undefined.

Answer 5

If you approach from the right, it goes to +∞
If you approach from the left, it goes to -∞
Since the right-side and left-side limits aren't equal, the limit doesn't exist.

Answer 6

If you try graphing it, it'll be identical to the graph of y=1/x except it'll also have a hole where the function isn't defined at x=2. There is a vertical asymptote at x=0 and a horizontal asymptote at y=0. You'll see that the two sides of the curve diverge at x=0.