# Find a limit that involves CDF (t distribution)

Is there a way to show $$\lim\limits_{x \to -\infty}xT_{\nu}(x)=0$$ where $$T_{\nu}(x)$$ is the CDF of Student's t distribution? Repetitive application of L'Hospital's rule to the fraction $$\frac{x}{1/T_{\nu}(x)}$$ does not work.