2.1.3 Calculation of limits

Problem: Find the limits of functions without using L'Hopital's rule. 1. \( \lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}+1}+\sqrt{x}}{\sqrt[5]{x^{3}+x}-2 x} \), 2. \( \lim _{x \rightarrow 0} \frac{\cos 2 x-\cos 4 x}{3 x^{2}} \) 3. \( \lim _{x \rightarrow \infty}\left(\frac{2 x+5}{1+2 x}\right)^{5 x} \).