To tak: zad5) [latex] lim_{n o infty} frac{n(sqrt{3n+2}+sqrt{3n})}{(sqrt{3n+2}-sqrt{3n})(sqrt{3n+2}+sqrt{3n})} = lim_{n o infty} frac{(sqrt{3n^3+2n^2}+sqrt{3n^3} }{3n+2-3n} =[/latex][latex]lim_{n o infty} frac{n(sqrt{3n+2}+sqrt{3n}) }{2} = +infty[/latex] b) [latex] lim_{n o infty} sqrt{n^2+3n} - n = lim_{n o infty} frac{n^2 + 3n - n^2}{sqrt{n^2+3n}+n} = lim_{n o infty} frac{ frac{3n}{n} }{ sqrt{frac{n^2}{n^2}+frac{3n}{n^2}} + frac{n}{n} } = [/latex][latex] frac{3}{1+1} = frac{3}{2} [/latex] c) [latex] lim_{n o infty} frac{frac{1+2n-1}{2}*n }{ frac{2+2n}{2}*n } = lim_{n o infty} frac{2n^2}{2} * frac{2}{2n^2+2n} = lim_{n o infty} frac{n}{n+1} = 1[/latex]
