Question

Ajutati ma va rog frumos !!!

Answer 1

Răspuns:

Explicație pas cu pas:

$\lim_{n \to \infty} (\frac{n^{2} +n-1}{n^{2}-n+1 } )^{n+3}$

$\lim_{n \to \infty} (\frac{n^{2} -n+1+2n-2}{n^{2}-n+1 } )^{n+3}=\lim_{n \to \infty} (1+\frac{2n-2}{n^{2} -n+1} )^{n+3}$

$=\lim_{n \to \infty}[ (1+\frac{2n-2}{n^{2} -n+1} )^{\frac{n^{2}-n+1 }{2n-2} } ]^{\frac{2n-2}{n^{2}-n+1 } } \cdot (n+3)$

$e^{ \lim_{n \to \infty} \frac{(2n-2)(n+3)}{n^{2} -n+1} }=e^{ \lim_{n \to \infty} \frac{2n^{2}+4n-6 }{n^{2} -n+1} }$

Avand acelasi grad, adica 2 si la numaratori si la numitor limita va fi 2

deci $e^{2}$ este raspunsul final