How do I evaluate $\lim _{x\to 0}\left(\csc^2\left(2x\right)-\frac{1}{4x^2}\right)$ without using L'Hopital?
Evaluate $\mathop {\lim }\limits_{x \to 0} \left( {{1 \over {{{\sin }^2}x}} - {1 \over {{x^2}}}} \right)$