Need help solving $\lim_{x\to \infty}\frac{\sqrt x}{\cos(2x)+6x}$ and $\lim_{x\to \infty}\frac{\sqrt x\ln(2x+1)}{\cos(2x)+6x}$

For the first I tried making it $\frac{\frac{1}{\cos(2x)+6x}}{\frac{1}{\sqrt x}}$ so it can be $\frac{0}{0}$ and do de l'hospital but it goes again at $\frac{0}{0}$ so I suppose I just dont know something hence the reason im asking this question.

and following that comes solving the second one.

I need to find their sum so I can find if it converges or diverges.