1.Sa se arate ca urmatoarele siruri ([tex] x_{n} [/tex]) au limita egala cu 0, stiind termenii lor generali:
a) [tex] x_{n} [/tex]=[tex] \frac{sin n + cos^{2} n }{n} [/tex]
b)[tex] x_{n} = \frac{n+1}{ n^{2} } [/tex]
c)[tex] x_{n} = \frac{ n^{2} }{ n^{3}+n+1 } [/tex]
2.Sa se calculeze urmatoarele limite:
a)[tex] \lim_{n \to \infty} ( \sqrt{ n^{2}+n+1 }-2n ) [/tex]
b)[tex] \lim_{n \to \infty} ( \sqrt[3]{ 2n^{3} +n - 1}-n )[/tex]
c)[tex] \lim_{n \to \infty} (-3n+ \sqrt{10 n^{2} -n+2} )[/tex]
d)[tex] \lim_{n \to \infty} (- \sqrt[3]{7 n^{3} +1}+2n )[/tex]
e)[tex] \lim_{n \to \infty} \frac{ n^{2}+n-2 }{(n+1)^3+ n^{3} } [/tex]