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Oblicz granice ciągów.
: 24 sty 2019, 23:58
autor: peresbmw
a) \(\sqrt{9^n+2*3^n}\) - \(\sqrt{9^n+4}\)
Re: Oblicz granice ciągów.
: 25 sty 2019, 09:27
autor: radagast
\(\Lim_{n\to \infty } \sqrt{9^n+2*3^n}-\sqrt{9^n+4}= \Lim_{n\to \infty } \frac{9^n+2*3^n-9^n-4}{\sqrt{9^n+2*3^n}+\sqrt{9^n+4}} = \Lim_{n\to \infty } \frac{2*3^n-4}{\sqrt{9^n+2*3^n}+\sqrt{9^n+4}} = \Lim_{n\to \infty } \frac{2- \frac{4}{3^n} }{\sqrt{1+ \frac{2}{9^n} }+\sqrt{1+ \frac{4}{9^n} }}= \frac{2}{1+1} =1\)