# Roots of the normal distribution

1. Nov 11, 2014

### BOAS

1. The problem statement, all variables and given/known data
$$f:\mathbb{R} \rightarrow \mathbb{R},$$

$$f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^2}{2 \sigma ^{2}}}$$

What are the roots of this equation?

2. Relevant equations

3. The attempt at a solution

The roots of an equation are the values of $x$ such that $f(x) = 0$. This is the first time I have seen a question like this and am still getting my head around the normal distribution, but as far as i'm aware the curve never does reach $f(x) = 0$ so I want to express the idea that the roots of this equation are $+/- \infty$ but I don't know how to do this...

$lim_{x \rightarrow +/- \infty} f(x) = 0$

I'd appreciate some guidance,

thanks :)

2. Nov 11, 2014

### LCKurtz

It doesn't look to me like you need much guidance on this. You have it exactly correct. But I wouldn't say the roots are $\pm \infty$. Just say it has no roots but the limit is 0 as you have stated.

3. Nov 11, 2014

### BOAS

Well that is good news, thanks!