# Thread: showing that limit is zero

1. ## showing that limit is zero

Hi there,

how can I prove that lim x->0 sqrt(abs(x)).sin(1/x) = 0?

2. Originally Posted by dgmath
Hi there,

how can I prove that lim x->0 sqrt(abs(x)).sin(1/x) = 0?
Squeeze theorem.

3. Originally Posted by dgmath
Hi there,

how can I prove that lim x->0 sqrt(abs(x)).sin(1/x) = 0?
$\displaystyle |\sqrt{|x|}sin\frac{1}{x}|\leq\sqrt{|x|}<\epsilon\ Longleftrightarrow|x|<\epsilon^2$.

So choose $\displaystyle \delta<\epsilon^2$

4. squeeze theorem it is! thanks!