calculating limit for a sech function is any answer in terms of dirac delta function?
how can i calculate this expression?
$$\lim_{x\to 0} {1\over \sqrt{x}} \text{sech} \left(\dfrac{1}{x}\right)$$

$\lim_{x\to 0} {1\over \sqrt{x}} \text{sech} \left(\dfrac{1}{x}\right)$
$=\dfrac{\frac{1}{\sqrt{x}}}{\cosh (\frac{1}{x})}$
$t=\frac{1}{x}$
$=\lim_{t\to \infty} \dfrac{\sqrt{t}}{\cosh (t)}$
Applying L'Hopital's rule:
$=\lim_{t\to \infty} \dfrac{1}{2\sqrt{t}\sinh{t}}$
$=\frac{1}{\infty}$
$=0$
