Limits

Calculate the limits provided below. If you decide to use L$\text{'}$H$$pital$\text{'}$s Rule, make sure to specify the type of indeterminate form that warrants its application.$($ could you explain step by step? And explantion? Im struggling and would like a step by step to help learn.. thank you.$)$

$($a$)$

$\underset{x}{lim}\frac{ln(2x)}{x^2}$

$($b$)$

$\underset{x{0}^{+}}{lim}csc(x)-cot(x)$