Mathematics - Continuity - Differentiability Question with Solution | TestHub

$f(x)$ is differentiable in $[0,1]$

${\underset{\mathrm{x}\to 0}{\lim }}_{}\frac{f(x)}{g(x)}$ does not exist

${\underset{\mathrm{x}\to 0}{\lim }}_{}{f}^{\prime }(x)g^{\prime }(x)$ does not exist

${\underset{\mathrm{x}\to 0}{\lim }}_{}\frac{f^{\prime }(x)}{g^{\prime }(x)}$ does not exist