# Thread: need confirmation of counterexample

1. ## need confirmation of counterexample

Hi! I have to find a counterexample to the following statement:
$\lim_{x\to \infty}f(\frac{1}{x})=L$ implies $\lim_{x\to 0}f(x)=L$

I assert that $f(x)=\left\{\begin{array}{lr}1:&x>0\\-1:&x\leq 0\end{array}\right\}$ is a viable counterexample.

Is this correct?
The limit at 0 does not exist, but the limit of f(x) as x goes to infinity will be 1.
Im just not 100% sure...
Any feedback would be appreciated.

2. Originally Posted by dannyboycurtis
Hi! I have to find a counterexample to the following statement:
$\lim_{x\to \infty}f(\frac{1}{x})=L$ implies $\lim_{x\to 0}f(x)=L$

I assert that $f(x)=\left\{\begin{array}{lr}1:&x>0\\-1:&x\leq 0\end{array}\right\}$ is a viable counterexample.

Is this correct?
The limit at 0 does not exist, but the limit of f(x) as x goes to infinity will be 1.
Im just not 100% sure...
Any feedback would be appreciated.

Nice, simple and neat example...oh, and correct, too.

Tonio