1. ## Simple limit...

It's unbelievable how much and how soon I can get rust if I don't keep doing math stuff.

I've this simple problem that I cannot resolve...

I cannot see which of the two functions prevales.

limit for x to 0 of [ ln(x^2) + 1/(x^2) ]

Thanks a bunch!

2. ## Re: Simple limit...

Originally Posted by paolopiace
It's unbelievable how much and how soon I can get rust if I don't keep doing math stuff.

I've this simple problem that I cannot resolve...

I cannot see which of the two functions prevales.

limit for x to 0 of [ ln(x^2) + 1/(x^2) ]

Thanks a bunch!
$\displaystyle \ln(x^2)+\frac{1}{x^2}=-\ln\left(\frac{1}{x^2}\right) +\frac{1}{x^2}$

Put $\displaystyle y=1/x^2$ then we have:

$\displaystyle \ln(x^2)+\frac{1}{x^2}=-\ln\left(y\right) +y$

Now $\displaystyle \ln(y)$ goes to infinity as $\displaystyle y$ becomes large more slowly than any polynomial in $\displaystyle y$, so eventually the $\displaystyle y$ dominates and the whole thing goes to infinity with $\displaystyle y$.

CB

3. ## Re: Simple limit...

Very much appreciated! Thank You...