Вычислите [latex]\displaystyle\lim_{x\rightarrow\infty}\frac{3x-1}{x^2+7x+5};\\ \lim_{x\rightarrow0,5}(2\arcsin x+3\arccos x).[/latex]

[latex] \lim\limits _{x \to \infty} \frac{3x-1}{x^2+7x+5} = \lim\limits _{x \to \infty} \frac{\frac{3}{x}-\frac{1}{x^2}}{1+\frac{7}{x}+\frac{5}{x^2}} =\frac{0}{1}=0\\\\ \lim\limits _{x \to 0,5} (2arcsinx+3arccosx)= \lim\limits _{x \to 0,5} (2arcsin0,5+3arccos0,5)=\\\\=2\cdot \frac{\pi}{6}+3\cdot \frac{\pi}{3}=\frac{\pi}{3}+\pi=\frac{4\pi}{3}[/latex]