Some Limits

1. Jun 17, 2007

americanforest

Hi, can somebody help me with this limit:

The Problem Statement:

limit as x approaches 1 from the left of ln(x(x-1)).

Attempt

I tried substitution and expansion in a Maclaurin series. This isn't homework its just a practice problem.

2. Jun 17, 2007

morphism

What's $\lim_{x->0^+} \ln x$?

3. Jun 17, 2007

americanforest

negative infinity

4. Jun 17, 2007

morphism

And what happens when we write ln(x(x-1)) = ln(x) + ln(x-1)?

5. Jun 17, 2007

americanforest

thats ln(1)+negative infinity so the limit is still negative infinity innit?

6. Jun 17, 2007

malawi_glenn

Yes. you can always confirm it by drawing the graph of the function on your Texas or Casio... or what you have

7. Jun 17, 2007

VietDao29

Well, when x approaches 1 from the left, the expression isn't even defined in the real, since x - 1 < 0, and hence x (x - 1) < 0. So ln(x (x - 1)) is not defined.

So, well, there's no limit from the left there. :)

8. Jun 17, 2007

malawi_glenn

aaa from the left, lol, i also thought it was from the right;)