Question

Lim(1+1/x)^5x вычислить лимит

Answer 1

$\lim_{x \to \infty} (1+ \frac{1}{x} ) ^{5x} = \lim_{x \to \infty} (1+ \frac{1}{x} ) ^{ \frac{x}{1}* \frac{1}{x} *5x } =( \lim_{x \to \infty} (1+ \frac{1}{x} )^{ \frac{x}{1} } )^{5} =e^{5}$