a)[latex]lim_{n o infty} 3n^2-n/n+1=lim_{n o infty}3n^2-1+1=\=lim_{n o infty}3n^2=+infty[/latex] b)[latex]lim_{n o infty}2^{-n}+3cdot 4^n/3^n+2^{2n+1}=lim_{n o infty}(1/2)^n+3cdot (4/3)^n+2cdot 4^n=\=lim_{n o infty} 4^n((1/8)^n+3cdot (1/3)^n+2)=+infty(0+0+2)=+infty[/latex] c)[latex]lim_{n o infty}(n-sqrt{n^2}+4)=lim_{n o infty}(n-n+4)=4[/latex] d)[latex]lim_{n o infty} (1-frac{1}{n^2})^n=lim_{n o infty} ((1-frac{1}{n})cdot (1+frac{1}{n}))^n=\=lim_{n o infty} (1-frac{1}{n})^ncdot (1+frac{1}{n})^n=e^{-1}*e^{1}=1[/latex]
Oblicz Granice : a)[latex] lim_{n o infty} (n- sqrt{n^{2} +2n)[/latex] b)[latex] lim_{x o 3} frac{x^{2}-9 }{x-3} [/latex]...
Oblicz granicę ciągu: [latex] lim_{n o infty}( sqrt{ n^{2}+7n-1 } )[/latex] [latex] lim_{n o infty} ( frac{3n+7}{8n+4} + frac{3n-4}{6n+5} )[/latex] [latex] lim_{n o infty} frac{ 3^{n}- 4^{n} }{ 5^{n}+ 4^{n} } [/latex] [latex] lim_{n o inft...
Oblicz granice: [latex] lim_{x o infty} ( frac{x^{3}-3x-2}{x^{2}-2x} -x) lim_{x o 0}( frac{1-sqrt{1-x} }{sin5x} lim_{x o infty} (x- sqrt{x^{2}-x+1} [/latex]...
Oblicz granice: [latex] lim_{n o infty} frac{n^3+2n-5}{(n- sqrt{n} )*(1-2n^2)} [/latex] [latex] lim_{n o infty} frac{(n+1)!( sqrt{4n^2-2n+3} -1)}{(n+1)!-(n+2)!} [/latex] Jeśli można to prosze o wytłumaczenie jak sie rozwiazuje tą silnię....
Oblicz granice [latex] lim_{n o infty} sqrt{ n+sqrt{n} } - sqrt{n- sqrt{n} } [/latex] [latex] lim_{n o infty} (1- frac{4}{n})^{-n+3} [/latex]...
