2.1.1 Calculation of limits

Problem: Compute the limits of the functions: 1. \( \lim _{x \rightarrow 2} \frac{2^{x}-x^{2}}{(x-2)^{2}} \), 2. \( \lim _{x \rightarrow 0} \frac{\tan ^{-1}(2 x)-\tan (2 x)}{x^{3}} \), 3. \( \lim _{x \rightarrow 0} \frac{x^{2}+2^{x}}{2 x^{3}-2} \).