Question

$\lim_{n \to \infty} (1+ \frac{1}{n^{2}+3} ) ^{5n^{2}}$

Answer 1

$\lim_{n \to \infty} (1+ \frac{1}{n^{2}+3} ) ^{5n^{2}} = \lim_{n \to \infty} (1+ \frac{1}{n^{2}+3} ) ^{ \frac{n^2+3}{({{5n^{2}})}*{({n^2+3}}})= [tex] \lim_{n \to \infty} (e) ^ \frac{(5n^{2})}{(n^2+3)}= \lim_{n \to \infty} (e ) ^ \frac{5}{1+\frac{3}{n^2}} = \lim_{n \to \infty} (e ) ^{5} =$