# Thread: Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

1. ## Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

I'm having a hard time visualizing it.

2. ## Re: Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

Originally Posted by gummy_ratz
I'm having a hard time visualizing it.
Maybe because $\displaystyle x$ is only defined for $\displaystyle x \in [0, 1]$... How can you possibly make $\displaystyle x\to\infty$ when the function does not even exist there?

3. ## Re: Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

The function doesnt exist as n->00? I'm looking for a function cont. on fn:[0,1]->[0,1] that fails to have a limit for every x in [0,1], and when integrating it from 0 to 1 as n->00 it equals 0. I thought I read somewhere that this fit the description?