w 1 na górze jest ciąg arytmetyczny [latex]S_n=frac{a_1+a_n}{2} cdot n = frac{1+n}{2} cdot n = frac{n+n^2}{2}[/latex] [latex]frac{frac{n+n^2}{2}}{n-2n^2}=frac{n+n^2}{2n-4n^2}=frac{n^2(frac{1}{n}+1)}{n^2(frac{2}{n}-4)}=frac{frac{1}{n}+1}{frac{2}{n}-4}[/latex] [latex] lim_{n o infty} (frac{frac{1}{n}+1}{frac{2}{n}-4}) = frac{0+1}{0-4}=-frac{1}{4} [/latex] 2. [latex]frac{2n^4-n^2+2}{3n^3+6}=frac{n^3(2n-frac{1}{n}+frac{2}{n^3})}{n^3(3+frac{6}{n^3})}=frac{2n-frac{1}{n}+frac{2}{n^3}}{3+frac{6}{n^3}}[/latex] [latex] lim_{n o infty} (frac{2n-frac{1}{n}+frac{2}{n^3}}{3+frac{6}{n^3}})=frac{infty-0+0}{3+0}=frac{infty}{3}=infty[/latex]
Oblicz granicę: a) [latex] lim_{x o+ infty} frac{1}{x^2-4x+3} [/latex] b) [latex] lim_{x o- infty} frac{1}{x^2-4x+3} [/latex]...
Oblicz granicę ciągu 1. [latex] lim_{n o infty} frac{sin (n)}{n^2 + 1} [/latex] 2. [latex] lim_{n o infty} frac{cos (n^5)}{n + 1} [/latex] Proszę o szczegółowe rozpisanie....
Oblicz granice: [latex]lim_{x o infty} frac{3 ^{x} }{(3 ^{x}-3 ^{2})x } [/latex] [latex] lim_{x o infty} frac{sin ^{2} x}{x^{4} } [/latex] [latex] lim_{x o infty} frac{cosx}{(e ^{x}+1)x } [/latex]...
Oblicz granice ciągów:[latex] lim_{n o infty} frac{(3^{n}-1)(2 ^{n}+4) }{ 5^{n}-6 ^{n} } lim_{n o infty} (3n- frac{1}{ n^{2} } )* frac{(2n-1) ^{2} }{(n+1) ^{3} } [/latex]...
Oblicz granice a) [latex] lim_{x o infty} frac{8 x^{3}-6x+8 }{2 x^{4}+2x-5 } [/latex] b) [latex] lim_{x o infty} (3 x^{3} -4 x^{2} +6)[/latex]...
