Finding the Limit as x Approaches 1 from the Left

[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.

 

[morphism]

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

 

[americanforest]

negative infinity

 

[morphism]

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

 

[americanforest]

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

 

[malawi_glenn]

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

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

 

[VietDao29]

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.

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. :)

 

[malawi_glenn]

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