MATEMATIKA 1 skripta studij: Biotehnologija i Prehrambena ... - PBF
MATEMATIKA 1 skripta studij: Biotehnologija i Prehrambena ... - PBF
MATEMATIKA 1 skripta studij: Biotehnologija i Prehrambena ... - PBF
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Zadatak 56<br />
lim<br />
n→∞<br />
( ) n 2 −n 2<br />
+n+1<br />
n 2 +n−1<br />
Rješenje:<br />
lim<br />
n→∞<br />
( ) n 2 −n 2 ( )<br />
+n+1 n 2 n 2<br />
+n−1<br />
= lim = (1 ∞ )<br />
n 2 +n−1 n→∞ n 2 +n+1<br />
(<br />
= lim 1+<br />
n→∞<br />
⎧⎡<br />
) n 2 ⎪⎨ (<br />
−2<br />
= lim ⎣ 1+<br />
n 2 +n+1 n→∞ ⎪ ⎩<br />
−2<br />
n 2 +n+1<br />
)n 2 +n+1<br />
−2<br />
⎤<br />
⎦<br />
−2<br />
n 2 +n+1<br />
⎫<br />
⎪⎬<br />
⎪⎭<br />
n 2<br />
= e lim<br />
n→∞<br />
−2n 2<br />
n 2 +n+1 = e −2 42
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