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Zadatak 0836

Test: MKsIVBGI_073

 

Izračunaj graničnu vrednost niza $$\lim \limits_{n \to +\infty }\left ( \frac{n^3}{n-5}-\frac{2n^4+n^3-4n^2+5}{2n^2-9n-5} \right )$$

 

Rešenje:


$$...=\lim \limits_{n \to +\infty }\frac{n^3(2n^2-9n-5)-(n-5)(2n^4+n^3-4n^2+5)}{(n-5)(2n^2-9n-5)}$$

$$=\lim \limits_{n \to +\infty }\frac{2n^5-9n^4-5n^3-2n^5-n^4+4n^3-5n+10n^4+5n^3-20n^2+25}{2n^3-9n^2-5n-10n^2+45n+25}$$

$$=\lim \limits_{n \to +\infty }\frac{4n^3-20n^2-5n+25}{2n^3-19n^2+40n+25}$$

$$=\lim \limits_{n \to +\infty }\frac{4-\frac{20}{n}-\frac{5}{n^2}+\frac{25}{n^3}}{2-\frac{19}{n}+\frac{40}{n^2}+\frac{25}{n^3}}$$

$$=2$$


 

 

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