L'Hopitals Rule

Limits can be calculated using this rule only if they take one of the two indeterminate forms:

\frac{0}{0} \frac{\pm \infty}{\pm \infty}

If the previous condition is met the derivative of the function in the numerator over the derivative of the function in the denominator will give you the value of the limit.

l i m_{x \to c} \frac{f (x)}{g (x)} = \frac{f^{'} (x)}{g^{'} (x)}

e.g. given $lim_{x \to 1} \frac{\cos (\frac{π}{2} x)}{\sin (π x)}$ the solution is as following:

lim_{x \to 1} \frac{\cos (\frac{π}{2} x)}{\sin (π x)} = lim_{x \to 1} \frac{- \frac{π}{2} \sin (\frac{π}{2} x)}{π \cos (π x)}

From there you can simply directly substitute to get the solution.