A very uncanny limit

[DariusBotusanu]

Hello gentleman, I have come yet again with another tricky question.
What is the result of:
[MATH]lim_(x->0)(a^((1)/(x)))*log(a))/(x^(2))[/MATH] ?
x<0

 

[Harry_the_cat]

Just sayin'. There are also some female helpers on this site, believe it or not!

 

[Dr.Peterson]

Hello gentleman, I have come yet again with another tricky question.
What is the result of:
[MATH]lim_(x->0)(a^((1)/(x)))*log(a))/(x^(2))[/MATH] ?
x<0

I think you mean

[MATH]\lim_{x\to 0}\frac{a^{1/x}\log(a)}{x^2}[/MATH]​

Are you saying that [MATH]x<0[/MATH] (that is, the limit approaches 0 from below), or did you mean [MATH]a<0[/MATH] (which would be a disaster)?

Can you show us what you have tried, so we can see what you consider tricky about it?

 

[pka]

Comment: the problem contains \(\log(a)\) so \(a>0\).

 

[JeffM]

Is your problem

[MATH]\left ( \lim_{x \rightarrow 0^-} \dfrac{a^{1/x} * log_{10}(a)}{x^2} \right )?[/MATH]
Are there constraints on a other than a > 0?

 

[Steven G]

I would like to know if a=1, a>1 or 0<a<1? Or possibly the limit has different results depending on the value of a.

 

[MarkFL]

I would like to know if the OP, upon seeing the result of their \(\LaTeX\), had a similar reaction to this:

 

[pka]

I think the same can be said of anyone who posts an image of their question.
It is not too much to ask that the post be done in ordinary type.
LaTeX is better, but I refuse to stand on my head to read an image post.